diff --git a/Project.toml b/Project.toml
index bacc0b72..47b9db86 100644
--- a/Project.toml
+++ b/Project.toml
@@ -10,7 +10,7 @@ SCIP_jll = "e5ac4fe4-a920-5659-9bf8-f9f73e9e79ce"
 
 [compat]
 Ipopt_jll = "^3.13.2"
-MathOptInterface = "^0.9.6"
+MathOptInterface = "0.10"
 SCIP_jll = "^0.1.2"
 julia = "1"
 
diff --git a/README.md b/README.md
index da923c5e..bf911925 100644
--- a/README.md
+++ b/README.md
@@ -88,7 +88,7 @@ features through MathOptInterface. However, the focus is on keeping the wrapper
 simple and avoiding duplicate storage of model data.
 
 As a consequence, we do not currently support some features such as retrieving
-constraints by name (`SingleVariable`-set constraints are not stored as SCIP
+constraints by name (`VariableIndex`-set constraints are not stored as SCIP
 constraints explicitly).
 
 Support for more constraint types (quadratic/SOC, SOS1/2, nonlinear expression)
diff --git a/src/MOI_wrapper.jl b/src/MOI_wrapper.jl
index 9efb401c..44ce32ae 100644
--- a/src/MOI_wrapper.jl
+++ b/src/MOI_wrapper.jl
@@ -6,7 +6,6 @@ const MOIU = MOI.Utilities
 const VI = MOI.VariableIndex
 const CI = MOI.ConstraintIndex
 # supported functions
-const SVF = MOI.SingleVariable
 const SAF = MOI.ScalarAffineFunction{Float64}
 const SQF = MOI.ScalarQuadraticFunction{Float64}
 const VAF = MOI.VectorAffineFunction{Float64}
@@ -44,8 +43,7 @@ mutable struct Optimizer <: MOI.AbstractOptimizer
 
         scip_data = SCIPData(scip, Dict(), Dict(), 0, 0, Dict(), Dict(), Dict())
 
-        o = new(scip_data, PtrMap(), ConsTypeMap(), Dict(), Dict(), Dict(),
-        nothing)
+        o = new(scip_data, PtrMap(), ConsTypeMap(), Dict(), Dict(), Dict(), nothing)
         finalizer(free_scip, o)
 
         # Set all parameters given as keyword arguments, replacing the
@@ -53,7 +51,7 @@ mutable struct Optimizer <: MOI.AbstractOptimizer
         # allowed in Julia identifiers.
         for (key, value) in kwargs
             name = replace(String(key),"_" => "/")
-            MOI.set(o, Param(name), value)
+            MOI.set(o, MOI.RawOptimizerAttribute(name), value)
         end
         return o
     end
@@ -135,16 +133,23 @@ end
 
 MOI.get(::Optimizer, ::MOI.SolverName) = "SCIP"
 
-MOIU.supports_default_copy_to(model::Optimizer, copy_names::Bool) = !copy_names
+MOI.supports_incremental_interface(::Optimizer) = true
+
+function _throw_if_invalid(o::Optimizer, ci::CI{F, S}) where {F, S}
+    if !in(ConsRef(ci.value), o.constypes[F, S])
+        throw(MOI.InvalidIndex(ci))
+    end
+    return nothing
+end
 
 # Keep SCIP-specific alias for backwards-compatibility.
-const Param = MOI.RawParameter
+const Param = MOI.RawOptimizerAttribute
 
-function MOI.get(o::Optimizer, param::MOI.RawParameter)
+function MOI.get(o::Optimizer, param::MOI.RawOptimizerAttribute)
     return get_parameter(o.inner, param.name)
 end
 
-function MOI.set(o::Optimizer, param::MOI.RawParameter, value)
+function MOI.set(o::Optimizer, param::MOI.RawOptimizerAttribute, value)
     o.params[param.name] = value
     set_parameter(o.inner, param.name, value)
     return nothing
@@ -153,11 +158,11 @@ end
 MOI.supports(o::Optimizer, ::MOI.Silent) = true
 
 function MOI.get(o::Optimizer, ::MOI.Silent)
-    return MOI.get(o, MOI.RawParameter("display/verblevel")) == 0
+    return MOI.get(o, MOI.RawOptimizerAttribute("display/verblevel")) == 0
 end
 
 function MOI.set(o::Optimizer, ::MOI.Silent, value)
-    param = MOI.RawParameter("display/verblevel")
+    param = MOI.RawOptimizerAttribute("display/verblevel")
     if value
         MOI.set(o, param, 0) # no output at all
     else
@@ -168,7 +173,7 @@ end
 MOI.supports(o::Optimizer, ::MOI.TimeLimitSec) = true
 
 function MOI.get(o::Optimizer, ::MOI.TimeLimitSec)
-    raw_value = MOI.get(o, MOI.RawParameter("limits/time"))
+    raw_value = MOI.get(o, MOI.RawOptimizerAttribute("limits/time"))
     if raw_value == SCIPinfinity(o)
         return nothing
     else
@@ -178,9 +183,9 @@ end
 
 function MOI.set(o::Optimizer, ::MOI.TimeLimitSec, value)
     if value === nothing
-        MOI.set(o, MOI.RawParameter("limits/time"), SCIPinfinity(o))
+        MOI.set(o, MOI.RawOptimizerAttribute("limits/time"), SCIPinfinity(o))
     else
-        MOI.set(o, MOI.RawParameter("limits/time"), value)
+        MOI.set(o, MOI.RawOptimizerAttribute("limits/time"), value)
     end
 end
 
@@ -213,8 +218,8 @@ function MOI.empty!(o::Optimizer)
     return nothing
 end
 
-function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike; kws...)
-    return MOIU.automatic_copy_to(dest, src; kws...)
+function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
+    return MOIU.default_copy_to(dest, src)
 end
 
 MOI.get(o::Optimizer, ::MOI.Name) = SCIPgetProbName(o)
@@ -224,10 +229,21 @@ function MOI.get(o::Optimizer, ::MOI.NumberOfConstraints{F,S}) where {F,S}
     return haskey(o.constypes, (F, S)) ? length(o.constypes[F, S]) : 0
 end
 
-function MOI.get(o::Optimizer, ::MOI.ListOfConstraints)
+function MOI.get(o::Optimizer, ::MOI.ListOfConstraintTypesPresent)
     return collect(keys(o.constypes))
 end
 
+function MOI.get(o::Optimizer, ::MOI.ListOfConstraintIndices{F, S}) where {F, S}
+    list_indices = Vector{CI{F,S}}()
+    if !haskey(o.constypes, (F, S))
+        return list_indices
+    end
+    for cref in o.constypes[F, S]
+        push!(list_indices, CI{F,S}(cref.val))
+    end
+    return sort!(list_indices, by=v->v.value)
+end
+
 function set_start_values(o::Optimizer)
     if isempty(o.start)
         # no primal start values are given
diff --git a/src/MOI_wrapper/abspower_constraints.jl b/src/MOI_wrapper/abspower_constraints.jl
index 36480f1f..3f2b7c27 100644
--- a/src/MOI_wrapper/abspower_constraints.jl
+++ b/src/MOI_wrapper/abspower_constraints.jl
@@ -47,6 +47,7 @@ function MOI.add_constraint(o::Optimizer, func::VECTOR, set::ABSPOWER)
 end
 
 function MOI.delete(o::Optimizer, ci::CI{VECTOR, ABSPOWER})
+    _throw_if_invalid(o, ci)
     allow_modification(o)
     delete!(o.constypes[VECTOR, ABSPOWER], ConsRef(ci.value))
     delete!(o.reference, cons(o, ci))
@@ -55,6 +56,7 @@ function MOI.delete(o::Optimizer, ci::CI{VECTOR, ABSPOWER})
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, ABSPOWER})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)::Ptr{SCIP_CONS}
     lvar = SCIPgetLinearVarAbspower(o, c)
     nlvar = SCIPgetNonlinearVarAbspower(o, c)
@@ -62,13 +64,12 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, ABSPOWER
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{VECTOR, ABSPOWER})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)::Ptr{SCIP_CONS}
-
     n = SCIPgetExponentAbspower(o, c)
     a = SCIPgetOffsetAbspower(o, c)
     coef = SCIPgetCoefLinearAbspower(o, c)
     lhs = SCIPgetLhsAbspower(o, c)
     rhs = SCIPgetRhsAbspower(o, c)
-
     return AbsolutePowerSet(n, a, coef, lhs, rhs)
 end
diff --git a/src/MOI_wrapper/constraints.jl b/src/MOI_wrapper/constraints.jl
index 0ff432d0..ea960170 100644
--- a/src/MOI_wrapper/constraints.jl
+++ b/src/MOI_wrapper/constraints.jl
@@ -8,3 +8,27 @@ function MOI.set(o::Optimizer, ::MOI.ConstraintName, ci::CI, name::String)
     @SCIP_CALL SCIPchgConsName(o, cons(o, ci), name)
     return nothing
 end
+
+function MOI.set(o::Optimizer, ::MOI.ConstraintName, ci::CI{VI}, name::String)
+    throw(MOI.VariableIndexConstraintNameError())
+    return nothing
+end
+
+function MOI.is_valid(o::Optimizer, c::CI{F, S}) where {F, S}
+    cons_set = get(o.constypes, (F, S), nothing)
+    if cons_set === nothing
+        return false
+    end
+    if !in(ConsRef(c.value), cons_set)
+        return false
+    end
+    return haskey(o.inner.conss, SCIP.ConsRef(c.value))
+end
+
+# function MOI.get(::Optimizer, ::MOI.ListOfConstraintAttributesSet{F, S}) where {F, S}
+#     return [MOI.ConstraintName()]
+# end
+
+# function MOI.get(::Optimizer, ::MOI.ListOfConstraintAttributesSet{<:Union{SAF, SQF}, S}) where {S}
+#     return Any[MOI.ConstraintName(), MOI.ConstraintPrimal()]
+# end
diff --git a/src/MOI_wrapper/indicator_constraints.jl b/src/MOI_wrapper/indicator_constraints.jl
index f02b7427..7f264545 100644
--- a/src/MOI_wrapper/indicator_constraints.jl
+++ b/src/MOI_wrapper/indicator_constraints.jl
@@ -1,34 +1,36 @@
 # Indicator constraints
 
-MOI.supports_constraint(::Optimizer, ::Type{<:MOI.VectorAffineFunction}, ::Type{<:MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, <:MOI.LessThan}}) = true
+MOI.supports_constraint(::Optimizer, ::Type{<:MOI.VectorAffineFunction}, ::Type{<:MOI.Indicator{MOI.ACTIVATE_ON_ONE, <:MOI.LessThan}}) = true
 
-function MOI.add_constraint(o::Optimizer, func::MOI.VectorAffineFunction{T}, set::MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, LT}) where {T<:Real, LT<:MOI.LessThan}
+function MOI.add_constraint(o::Optimizer, func::MOI.VectorAffineFunction{T}, set::MOI.Indicator{MOI.ACTIVATE_ON_ONE, LT}) where {T<:Real, LT<:MOI.LessThan}
     allow_modification(o)
     first_index_terms  = [v.scalar_term for v in func.terms if v.output_index == 1]
     scalar_index_terms = [v.scalar_term for v in func.terms if v.output_index != 1]
     length(first_index_terms) == 1 || error("There should be exactly one term in output_index 1, found $(length(first_index_terms))")
-    y = VarRef(first_index_terms[1].variable_index.value)
-    x = [VarRef(vi.variable_index.value) for vi in scalar_index_terms]
+    y = VarRef(first_index_terms[1].variable.value)
+    x = [VarRef(vi.variable.value) for vi in scalar_index_terms]
     a = [vi.coefficient for vi in scalar_index_terms]
     b = func.constants[2]
     # a^T x + b <= c ===> a^T <= c - b
 
     cr = add_indicator_constraint(o.inner, y, x, a, MOI.constant(set.set) - b)
-    ci = CI{MOI.VectorAffineFunction{T}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, LT}}(cr.val)
+    ci = CI{MOI.VectorAffineFunction{T}, MOI.Indicator{MOI.ACTIVATE_ON_ONE, LT}}(cr.val)
     register!(o, ci)
     register!(o, cons(o, ci), cr)
     return ci
 end
 
-function MOI.delete(o::Optimizer, ci::CI{MOI.VectorAffineFunction{T}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, LT}}) where {T<:Real, LT<:MOI.LessThan}
+function MOI.delete(o::Optimizer, ci::CI{MOI.VectorAffineFunction{T}, MOI.Indicator{MOI.ACTIVATE_ON_ONE, LT}}) where {T<:Real, LT<:MOI.LessThan}
+    _throw_if_invalid(o, ci)
     allow_modification(o)
-    delete!(o.constypes[MOI.VectorAffineFunction{T}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, LT}], ConsRef(ci.value))
+    delete!(o.constypes[MOI.VectorAffineFunction{T}, MOI.Indicator{MOI.ACTIVATE_ON_ONE, LT}], ConsRef(ci.value))
     delete!(o.reference, cons(o, ci))
     delete(o.inner, ConsRef(ci.value))
     return nothing
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{MOI.VectorAffineFunction{T}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, LT}}) where {T<:Real, LT<:MOI.LessThan}
+function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{MOI.VectorAffineFunction{T}, MOI.Indicator{MOI.ACTIVATE_ON_ONE, LT}}) where {T<:Real, LT<:MOI.LessThan}
+    _throw_if_invalid(o, ci)
     indicator_cons = cons(o, ci)::Ptr{SCIP_CONS}
     bin_var = SCIPgetBinaryVarIndicator(indicator_cons)::Ptr{SCIP_VAR}
     slack_var = SCIPgetSlackVarIndicator(indicator_cons)::Ptr{SCIP_VAR}
@@ -46,7 +48,8 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{MOI.VectorAffine
     return VAF(vcat(ind_terms, vec_terms), [0.0, 0.0])
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{MOI.VectorAffineFunction{T}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, LT}}) where {T<:Real, LT<:MOI.LessThan}
+function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{MOI.VectorAffineFunction{T}, MOI.Indicator{MOI.ACTIVATE_ON_ONE, LT}}) where {T<:Real, LT<:MOI.LessThan}
+    _throw_if_invalid(o, ci)
     indicator_cons = cons(o, ci)::Ptr{SCIP_CONS}
     linear_cons = SCIPgetLinearConsIndicator(indicator_cons)::Ptr{SCIP_CONS}
 
@@ -54,5 +57,9 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{MOI.VectorAffineFunct
     rhs = SCIPgetRhsLinear(o, linear_cons)
     lhs == -SCIPinfinity(o) || error("Have lower bound on indicator constraint!")
 
-    return MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(rhs))
+    return MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(rhs))
+end
+
+function MOI.get(o::Optimizer, ::MOI.ListOfConstraintIndices{F, S}) where {F <: MOI.VectorAffineFunction{Float64}, S <: MOI.Indicator{MOI.ACTIVATE_ON_ONE, MOI.LessThan{Float64}}}
+    return Vector{F, S}(o.constypes[F,S])
 end
diff --git a/src/MOI_wrapper/linear_constraints.jl b/src/MOI_wrapper/linear_constraints.jl
index 348e1b31..711f505e 100644
--- a/src/MOI_wrapper/linear_constraints.jl
+++ b/src/MOI_wrapper/linear_constraints.jl
@@ -2,14 +2,14 @@
 
 MOI.supports_constraint(o::Optimizer, ::Type{SAF}, ::Type{<:BOUNDS}) = true
 
-function MOI.add_constraint(o::Optimizer, func::SAF, set::S) where {S <: BOUNDS}
+function MOI.add_constraint(o::Optimizer, func::F, set::S) where {F <: SAF, S <: BOUNDS}
     if func.constant != 0.0
         error("SCIP does not support linear constraints with a constant offset.")
     end
 
     allow_modification(o)
 
-    varrefs = [VarRef(t.variable_index.value) for t in func.terms]
+    varrefs = [VarRef(t.variable.value) for t in func.terms]
     coefs = [t.coefficient for t in func.terms]
 
     lhs, rhs = bounds(set)
@@ -17,13 +17,14 @@ function MOI.add_constraint(o::Optimizer, func::SAF, set::S) where {S <: BOUNDS}
     rhs = rhs === nothing ?  SCIPinfinity(o) : rhs
 
     cr = add_linear_constraint(o.inner, varrefs, coefs, lhs, rhs)
-    ci = CI{SAF, S}(cr.val)
+    ci = CI{F, S}(cr.val)
     register!(o, ci)
     register!(o, cons(o, ci), cr)
     return ci
 end
 
-function MOI.delete(o::Optimizer, ci::CI{SAF, S}) where {S <: BOUNDS}
+function MOI.delete(o::Optimizer, ci::CI{<:SAF, S}) where {S <: BOUNDS}
+    _throw_if_invalid(o, ci)
     allow_modification(o)
     delete!(o.constypes[SAF, S], ConsRef(ci.value))
     delete!(o.reference, cons(o, ci))
@@ -31,7 +32,7 @@ function MOI.delete(o::Optimizer, ci::CI{SAF, S}) where {S <: BOUNDS}
     return nothing
 end
 
-function MOI.set(o::SCIP.Optimizer, ::MOI.ConstraintSet, ci::CI{SAF,S}, set::S) where {S <: BOUNDS}
+function MOI.set(o::SCIP.Optimizer, ::MOI.ConstraintSet, ci::CI{<:SAF,S}, set::S) where {S <: BOUNDS}
     allow_modification(o)
 
     lhs, rhs = bounds(set)
@@ -44,7 +45,8 @@ function MOI.set(o::SCIP.Optimizer, ::MOI.ConstraintSet, ci::CI{SAF,S}, set::S)
     return nothing
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{SAF, S}) where S <: BOUNDS
+function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{<:SAF, S}) where {S <: BOUNDS}
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)
     nvars::Int = SCIPgetNVarsLinear(o, c)
     vars = unsafe_wrap(Array{Ptr{SCIP_VAR}}, SCIPgetVarsLinear(o, c), nvars)
@@ -55,13 +57,14 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{SAF, S}) where S
     return SAF(terms, 0.0)
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{SAF, S}) where S <: BOUNDS
+function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{<:SAF, S}) where {S <: BOUNDS}
+    _throw_if_invalid(o, ci)
     lhs = SCIPgetLhsLinear(o, cons(o, ci))
     rhs = SCIPgetRhsLinear(o, cons(o, ci))
     return from_bounds(S, lhs, rhs)
 end
 
-function MOI.modify(o::Optimizer, ci::CI{SAF, <:BOUNDS},
+function MOI.modify(o::Optimizer, ci::CI{<:SAF, <:BOUNDS},
                     change::MOI.ScalarCoefficientChange{Float64})
     allow_modification(o)
     @SCIP_CALL SCIPchgCoefLinear(o, cons(o, ci), var(o, change.variable), change.new_coefficient)
diff --git a/src/MOI_wrapper/objective.jl b/src/MOI_wrapper/objective.jl
index f9f51e9c..18c014db 100644
--- a/src/MOI_wrapper/objective.jl
+++ b/src/MOI_wrapper/objective.jl
@@ -6,7 +6,7 @@
 
 MOI.supports(::Optimizer, ::MOI.ObjectiveSense) = true
 MOI.supports(::Optimizer, ::MOI.ObjectiveFunction{SAF}) = true
-MOI.supports(::Optimizer, ::MOI.ObjectiveFunction{SVF}) = true
+MOI.supports(::Optimizer, ::MOI.ObjectiveFunction{VI}) = true
 
 function MOI.set(o::Optimizer, ::MOI.ObjectiveFunction{SAF}, obj::SAF)
     allow_modification(o)
@@ -18,7 +18,7 @@ function MOI.set(o::Optimizer, ::MOI.ObjectiveFunction{SAF}, obj::SAF)
 
     # set new objective coefficients, summing coefficients
     for t in obj.terms
-        v = var(o, t.variable_index)
+        v = var(o, t.variable)
         oldcoef = SCIPvarGetObj(v)
         newcoef = oldcoef + t.coefficient
         @SCIP_CALL SCIPchgVarObj(o, v, newcoef)
@@ -30,8 +30,8 @@ function MOI.set(o::Optimizer, ::MOI.ObjectiveFunction{SAF}, obj::SAF)
 end
 
 # Note that SCIP always uses a scalar affine function internally!
-function MOI.set(o::Optimizer, ::MOI.ObjectiveFunction{SVF}, obj::SVF)
-    aff_obj = SAF([AFF_TERM(1.0, obj.variable)], 0.0)
+function MOI.set(o::Optimizer, ::MOI.ObjectiveFunction{VI}, obj::VI)
+    aff_obj = SAF([AFF_TERM(1.0, obj)], 0.0)
     return MOI.set(o, MOI.ObjectiveFunction{SAF}(), aff_obj)
 end
 
@@ -47,14 +47,14 @@ function MOI.get(o::Optimizer, ::MOI.ObjectiveFunction{SAF})
 end
 
 # Note that SCIP always uses a scalar affine function internally!
-function MOI.get(o::Optimizer, ::MOI.ObjectiveFunction{SVF})
+function MOI.get(o::Optimizer, ::MOI.ObjectiveFunction{VI})
     aff_obj = MOI.get(o, MOI.ObjectiveFunction{SAF}())
     if (length(aff_obj.terms) != 1
         || aff_obj.terms[1].coefficient != 1.0
         || aff_obj.constant != 0.0)
-        error("Objective is not single variable: $aff_obj !")
+        throw(InexactError(:get, VI, aff_obj))
     end
-    return SVF(aff_obj.terms[1].variable_index)
+    return aff_obj.terms[1].variable
 end
 
 function MOI.set(o::Optimizer, ::MOI.ObjectiveSense, sense::MOI.OptimizationSense)
@@ -63,7 +63,7 @@ function MOI.set(o::Optimizer, ::MOI.ObjectiveSense, sense::MOI.OptimizationSens
         @SCIP_CALL SCIPsetObjsense(o, SCIP_OBJSENSE_MINIMIZE)
     elseif sense == MOI.MAX_SENSE
         @SCIP_CALL SCIPsetObjsense(o, SCIP_OBJSENSE_MAXIMIZE)
-    elseif sense == MOI.FEASIBLITY_SENSE
+    elseif sense == MOI.FEASIBILITY_SENSE
         @warn "FEASIBLITY_SENSE not supported by SCIP.jl" maxlog=1
     end
     return nothing
diff --git a/src/MOI_wrapper/quadratic_constraints.jl b/src/MOI_wrapper/quadratic_constraints.jl
index 9eb081bb..b1a5e676 100644
--- a/src/MOI_wrapper/quadratic_constraints.jl
+++ b/src/MOI_wrapper/quadratic_constraints.jl
@@ -10,12 +10,12 @@ function MOI.add_constraint(o::Optimizer, func::SQF, set::S) where {S <: BOUNDS}
     allow_modification(o)
 
     # affine terms
-    linrefs = [VarRef(t.variable_index.value) for t in func.affine_terms]
+    linrefs = [VarRef(t.variable.value) for t in func.affine_terms]
     lincoefs = [t.coefficient for t in func.affine_terms]
 
     # quadratic terms
-    quadrefs1 = [VarRef(t.variable_index_1.value) for t in func.quadratic_terms]
-    quadrefs2 = [VarRef(t.variable_index_2.value) for t in func.quadratic_terms]
+    quadrefs1 = [VarRef(t.variable_1.value) for t in func.quadratic_terms]
+    quadrefs2 = [VarRef(t.variable_2.value) for t in func.quadratic_terms]
     # Divide coefficients by 2 iff they come from the diagonal:
     # Take coef * x * y as-is, but turn coef * x^2 into coef/2 * x^2.
     factor = 1.0 .- 0.5 * (quadrefs1 .== quadrefs2)
@@ -35,6 +35,7 @@ function MOI.add_constraint(o::Optimizer, func::SQF, set::S) where {S <: BOUNDS}
 end
 
 function MOI.delete(o::Optimizer, ci::CI{SQF, S}) where {S <: BOUNDS}
+    _throw_if_invalid(o, ci)
     allow_modification(o)
     delete!(o.constypes[SQF, S], ConsRef(ci.value))
     delete!(o.reference, cons(o, ci))
@@ -55,13 +56,8 @@ function MOI.set(o::SCIP.Optimizer, ::MOI.ConstraintSet, ci::CI{SQF,S}, set::S)
     return nothing
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{SQF, S}) where S <: BOUNDS
-    lhs = SCIPgetLhsQuadratic(o, cons(o, ci))
-    rhs = SCIPgetRhsQuadratic(o, cons(o, ci))
-    return from_bounds(S, lhs, rhs)
-end
-
-function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{SQF, S}) where S <: BOUNDS
+function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{SQF, S}) where {S <: BOUNDS}
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)
 
     affterms = AFF_TERM[]
@@ -93,10 +89,17 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{SQF, S}) where S
         push!(quadterms, QUAD_TERM(term.coef, VI(ref(o, term.var1).val), VI(ref(o, term.var2).val)))
     end
 
-    return SQF(affterms, quadterms, 0.0)
+    return SQF(quadterms, affterms, 0.0)
+end
+
+function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{SQF, S}) where {S <: BOUNDS}
+    _throw_if_invalid(o, ci)
+    lhs = SCIPgetLhsQuadratic(o, cons(o, ci))
+    rhs = SCIPgetRhsQuadratic(o, cons(o, ci))
+    return from_bounds(S, lhs, rhs)
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintPrimal, ci::CI{SQF, S}) where S <: BOUNDS
+function MOI.get(o::Optimizer, ::MOI.ConstraintPrimal, ci::CI{SQF, S}) where {S <: BOUNDS}
     activity = Ref{Cdouble}()
     @SCIP_CALL SCIPgetActivityQuadratic(o, cons(o, ci), SCIPgetBestSol(o), activity)
     return activity[]
diff --git a/src/MOI_wrapper/results.jl b/src/MOI_wrapper/results.jl
index f685fea1..a973978f 100644
--- a/src/MOI_wrapper/results.jl
+++ b/src/MOI_wrapper/results.jl
@@ -24,7 +24,7 @@ function MOI.get(o::Optimizer, ::MOI.TerminationStatus)
 end
 
 function MOI.get(o::Optimizer, attr::MOI.PrimalStatus)
-    return if 1 <= attr.N <= MOI.get(o, MOI.ResultCount())
+    return if 1 <= attr.result_index <= MOI.get(o, MOI.ResultCount())
         MOI.FEASIBLE_POINT
     else
         MOI.NO_SOLUTION
@@ -83,21 +83,21 @@ function MOI.get(o::Optimizer, attr::MOI.VariablePrimal, vi::VI)
     assert_solved(o)
     MOI.check_result_index_bounds(o, attr)
     sols = unsafe_wrap(Array{Ptr{SCIP_SOL}}, SCIPgetSols(o), SCIPgetNSols(o))
-    return SCIPgetSolVal(o, sols[attr.N], var(o, vi))
+    return SCIPgetSolVal(o, sols[attr.result_index], var(o, vi))
 end
 
-function MOI.get(o::Optimizer, attr::MOI.ConstraintPrimal, ci::CI{SVF,<:BOUNDS})
+function MOI.get(o::Optimizer, attr::MOI.ConstraintPrimal, ci::CI{VI,<:BOUNDS})
     assert_solved(o)
     MOI.check_result_index_bounds(o, attr)
     sols = unsafe_wrap(Array{Ptr{SCIP_SOL}}, SCIPgetSols(o), SCIPgetNSols(o))
-    return SCIPgetSolVal(o, sols[attr.N], var(o, VI(ci.value)))
+    return SCIPgetSolVal(o, sols[attr.result_index], var(o, VI(ci.value)))
 end
 
-function MOI.get(o::Optimizer, attr::MOI.ConstraintPrimal, ci::CI{SAF,<:BOUNDS})
+function MOI.get(o::Optimizer, attr::MOI.ConstraintPrimal, ci::CI{<:SAF,<:BOUNDS})
     assert_solved(o)
     MOI.check_result_index_bounds(o, attr)
     sols = unsafe_wrap(Array{Ptr{SCIP_SOL}}, SCIPgetSols(o), SCIPgetNSols(o))
-    return SCIPgetActivityLinear(o, cons(o, ci), sols[attr.N])
+    return SCIPgetActivityLinear(o, cons(o, ci), sols[attr.result_index])
 end
 
 function MOI.get(o::Optimizer, ::MOI.ObjectiveBound)
@@ -110,7 +110,7 @@ function MOI.get(o::Optimizer, ::MOI.RelativeGap)
     return SCIPgetGap(o)
 end
 
-function MOI.get(o::Optimizer, ::MOI.SolveTime)
+function MOI.get(o::Optimizer, ::MOI.SolveTimeSec)
     return SCIPgetSolvingTime(o)
 end
 
diff --git a/src/MOI_wrapper/sepa.jl b/src/MOI_wrapper/sepa.jl
index d7392538..91d594cd 100644
--- a/src/MOI_wrapper/sepa.jl
+++ b/src/MOI_wrapper/sepa.jl
@@ -78,8 +78,8 @@ end
 MOI.supports(::Optimizer, ::MOI.UserCutCallback) = true
 
 function MOI.submit(o::Optimizer, cb_data::MOI.UserCut{CutCbData},
-                    func::SAF, set::S) where S <: BOUNDS
-    varrefs = [VarRef(t.variable_index.value) for t in func.terms]
+                    func::SAF, set::S) where {S <: BOUNDS}
+    varrefs = [VarRef(t.variable.value) for t in func.terms]
     coefs = [t.coefficient for t in func.terms]
 
     lhs, rhs = bounds(set)
diff --git a/src/MOI_wrapper/soc_constraints.jl b/src/MOI_wrapper/soc_constraints.jl
index 6357c338..f317ce8e 100644
--- a/src/MOI_wrapper/soc_constraints.jl
+++ b/src/MOI_wrapper/soc_constraints.jl
@@ -21,6 +21,7 @@ function MOI.add_constraint(o::Optimizer, func::VECTOR, set::SOC)
 end
 
 function MOI.delete(o::Optimizer, ci::CI{VECTOR, SOC})
+    _throw_if_invalid(o, ci)
     allow_modification(o)
     delete!(o.constypes[VECTOR, SOC], ConsRef(ci.value))
     delete!(o.reference, cons(o, ci))
@@ -29,6 +30,7 @@ function MOI.delete(o::Optimizer, ci::CI{VECTOR, SOC})
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, SOC})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)::Ptr{SCIP_CONS}
     nvars::Int = SCIPgetNLhsVarsSOC(o, c)
     vars = unsafe_wrap(Array{Ptr{SCIP_VAR}}, SCIPgetLhsVarsSOC(o, c), nvars)
@@ -39,6 +41,7 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, SOC})
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{VECTOR, SOC})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)::Ptr{SCIP_CONS}
     nvars::Int = SCIPgetNLhsVarsSOC(o, c)
     return MOI.SecondOrderCone(nvars + 1)
diff --git a/src/MOI_wrapper/sos_constraints.jl b/src/MOI_wrapper/sos_constraints.jl
index 3c96583c..377f5e37 100644
--- a/src/MOI_wrapper/sos_constraints.jl
+++ b/src/MOI_wrapper/sos_constraints.jl
@@ -14,6 +14,7 @@ function MOI.add_constraint(o::Optimizer, func::VECTOR, set::SOS1)
 end
 
 function MOI.delete(o::Optimizer, ci::CI{VECTOR, SOS1})
+    _throw_if_invalid(o, ci)
     allow_modification(o)
     delete!(o.constypes[VECTOR, SOS1], ConsRef(ci.value))
     delete!(o.reference, cons(o, ci))
@@ -22,6 +23,7 @@ function MOI.delete(o::Optimizer, ci::CI{VECTOR, SOS1})
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, SOS1})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)
     nvars::Int = SCIPgetNVarsSOS1(o, c)
     vars = unsafe_wrap(Array{Ptr{SCIP_VAR}}, SCIPgetVarsSOS1(o, c), nvars)
@@ -29,6 +31,7 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, SOS1})
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{VECTOR, SOS1})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)
     nvars::Int = SCIPgetNVarsSOS1(o, c)
     weights = unsafe_wrap(Array{Float64}, SCIPgetWeightsSOS1(o, c), nvars)
@@ -51,6 +54,7 @@ function MOI.add_constraint(o::Optimizer, func::VECTOR, set::SOS2)
 end
 
 function MOI.delete(o::Optimizer, ci::CI{VECTOR, SOS2})
+    _throw_if_invalid(o, ci)
     allow_modification(o)
     delete!(o.constypes[VECTOR, SOS2], ConsRef(ci.value))
     delete!(o.reference, cons(o, ci))
@@ -59,6 +63,7 @@ function MOI.delete(o::Optimizer, ci::CI{VECTOR, SOS2})
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, SOS2})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)
     nvars::Int = SCIPgetNVarsSOS2(o, c)
     vars = unsafe_wrap(Array{Ptr{SCIP_VAR}}, SCIPgetVarsSOS2(o, c), nvars)
@@ -66,6 +71,7 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VECTOR, SOS2})
 end
 
 function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{VECTOR, SOS2})
+    _throw_if_invalid(o, ci)
     c = cons(o, ci)
     nvars::Int = SCIPgetNVarsSOS2(o, c)
     weights = unsafe_wrap(Array{Float64}, SCIPgetWeightsSOS2(o, c), nvars)
diff --git a/src/MOI_wrapper/variable.jl b/src/MOI_wrapper/variable.jl
index a73e746e..92ed4be1 100644
--- a/src/MOI_wrapper/variable.jl
+++ b/src/MOI_wrapper/variable.jl
@@ -10,7 +10,7 @@ end
 
 MOI.add_variables(o::Optimizer, n) = [MOI.add_variable(o) for i=1:n]
 MOI.get(o::Optimizer, ::MOI.NumberOfVariables) = length(o.inner.vars)
-MOI.get(o::Optimizer, ::MOI.ListOfVariableIndices) = [VI(k.val) for k in keys(o.inner.vars)]
+MOI.get(o::Optimizer, ::MOI.ListOfVariableIndices) = sort!([VI(k.val) for k in keys(o.inner.vars)], by=v->v.value)
 MOI.is_valid(o::Optimizer, vi::VI) = haskey(o.inner.vars, VarRef(vi.value))
 
 function MOI.get(o::Optimizer, ::MOI.VariableName, vi::VI)::String
@@ -30,8 +30,14 @@ function MOI.delete(o::Optimizer, vi::VI)
     if length(o.inner.conss) > 0
         error("Can not delete variable while model contains constraints!")
     end
-
     allow_modification(o)
+    if !haskey(o.inner.vars, VarRef(vi.value))
+        throw(MOI.InvalidIndex(vi))
+    end
+    # TODO still necessary?
+    if !haskey(o.reference, var(o, vi))
+        throw(MOI.InvalidIndex(vi))
+    end
     haskey(o.binbounds, vi) && delete!(o.binbounds, vi)
     delete!(o.reference, var(o, vi))
     delete(o.inner, VarRef(vi.value))
@@ -40,14 +46,13 @@ end
 
 ## variable types (binary, integer)
 
-MOI.supports_constraint(o::Optimizer, ::Type{SVF}, ::Type{<:VAR_TYPES}) = true
+MOI.supports_constraint(o::Optimizer, ::Type{VI}, ::Type{<:VAR_TYPES}) = true
 
 scip_vartype(::Type{MOI.ZeroOne}) = SCIP_VARTYPE_BINARY
 scip_vartype(::Type{MOI.Integer}) = SCIP_VARTYPE_INTEGER
 
-function MOI.add_constraint(o::Optimizer, func::SVF, set::S) where {S <: VAR_TYPES}
+function MOI.add_constraint(o::Optimizer, vi::VI, set::S) where {S <: VAR_TYPES}
     allow_modification(o)
-    vi = func.variable
     v = var(o, vi)
     infeasible = Ref{SCIP_Bool}()
     @SCIP_CALL SCIPchgVarType(o, v, scip_vartype(S), infeasible)
@@ -74,11 +79,12 @@ function MOI.add_constraint(o::Optimizer, func::SVF, set::S) where {S <: VAR_TYP
         end
     end
     # use var index for cons index of this type
-    i = func.variable.value
-    return register!(o, CI{SVF, S}(i))
+    i = vi.value
+    return register!(o, CI{VI, S}(i))
 end
 
-function MOI.delete(o::Optimizer, ci::CI{SVF,S}) where {S <: VAR_TYPES}
+function MOI.delete(o::Optimizer, ci::CI{VI,S}) where {S <: VAR_TYPES}
+    _throw_if_invalid(o, ci)
     allow_modification(o)
 
     vi = VI(ci.value)
@@ -92,26 +98,27 @@ function MOI.delete(o::Optimizer, ci::CI{SVF,S}) where {S <: VAR_TYPES}
     @SCIP_CALL SCIPchgVarType(o, var(o, vi), SCIP_VARTYPE_CONTINUOUS, infeasible)
     # TODO: warn if infeasible[] == TRUE?
 
-    # Can only change bounds after chaging the var type.
+    # Can only change bounds after changing the var type.
     if reset_bounds
-        bounds = o.binbounds[vi]
-        @SCIP_CALL SCIPchgVarLb(o, v, bounds.lower)
-        @SCIP_CALL SCIPchgVarUb(o, v, bounds.upper)
+        bounds = get(o.binbounds, vi, nothing)
+        if bounds !== nothing
+            @SCIP_CALL SCIPchgVarLb(o, v, bounds.lower)
+            @SCIP_CALL SCIPchgVarUb(o, v, bounds.upper)
+        end
     end
 
     # but do delete the constraint reference
-    delete!(o.constypes[SVF, S], ConsRef(ci.value))
+    delete!(o.constypes[VI, S], ConsRef(ci.value))
 
     return nothing
 end
 
 ## variable bounds
 
-MOI.supports_constraint(o::Optimizer, ::Type{SVF}, ::Type{<:BOUNDS}) = true
+MOI.supports_constraint(o::Optimizer, ::Type{VI}, ::Type{<:BOUNDS}) = true
 
-function MOI.add_constraint(o::Optimizer, func::SVF, set::S) where S <: BOUNDS
+function MOI.add_constraint(o::Optimizer, vi::VI, set::S) where {S <: BOUNDS}
     allow_modification(o)
-    vi = func.variable
     v = var(o, vi)
     inf = SCIPinfinity(o)
 
@@ -141,7 +148,8 @@ function MOI.add_constraint(o::Optimizer, func::SVF, set::S) where S <: BOUNDS
                 @debug "Overwriting existing bounds [0.0,1.0] with [$newlb,$newub] for binary variable at $(vi.value)!"
             end
         else # general case (non-binary variable)
-            error("Already have bounds [$oldlb,$oldub] for variable at $(vi.value)!")
+            # TODO find initially-set bound constraint
+            throw(MOI.LowerBoundAlreadySet{S,S}(vi))
         end
     end
 
@@ -154,25 +162,26 @@ function MOI.add_constraint(o::Optimizer, func::SVF, set::S) where S <: BOUNDS
     end
 
     # use var index for cons index of this type
-    i = func.variable.value
-    return register!(o, CI{SVF, S}(i))
+    i = vi.value
+    return register!(o, CI{VI, S}(i))
 end
 
-function reset_bounds(o::Optimizer, v, lb, ub, ci::CI{SVF, S}) where S <: Union{MOI.Interval{Float64}, MOI.EqualTo{Float64}}
+function reset_bounds(o::Optimizer, v, lb, ub, ci::CI{VI, S}) where S <: Union{MOI.Interval{Float64}, MOI.EqualTo{Float64}}
     @SCIP_CALL SCIPchgVarLb(o, v, lb)
     @SCIP_CALL SCIPchgVarUb(o, v, ub)
 end
 
-function reset_bounds(o::Optimizer, v, lb, ub, ci::CI{SVF, MOI.GreaterThan{Float64}})
+function reset_bounds(o::Optimizer, v, lb, ub, ci::CI{VI, MOI.GreaterThan{Float64}})
     @SCIP_CALL SCIPchgVarLb(o, v, lb)
 end
 
-function reset_bounds(o::Optimizer, v, lb, ub, ci::CI{SVF, MOI.LessThan{Float64}})
+function reset_bounds(o::Optimizer, v, lb, ub, ci::CI{VI, MOI.LessThan{Float64}})
     @SCIP_CALL SCIPchgVarUb(o, v, ub)
 end
 
 
-function MOI.delete(o::Optimizer, ci::CI{SVF,S}) where S <: BOUNDS
+function MOI.delete(o::Optimizer, ci::CI{VI,S}) where {S <: BOUNDS}
+    _throw_if_invalid(o, ci)
     allow_modification(o)
 
     # Don't actually delete any SCIP constraint, just reset bounds
@@ -187,12 +196,12 @@ function MOI.delete(o::Optimizer, ci::CI{SVF,S}) where S <: BOUNDS
 
     # but do delete the constraint reference
     haskey(o.binbounds, vi) && delete!(o.binbounds, vi)
-    delete!(o.constypes[SVF, S], ConsRef(ci.value))
+    delete!(o.constypes[VI, S], ConsRef(ci.value))
 
     return nothing
 end
 
-function MOI.set(o::SCIP.Optimizer, ::MOI.ConstraintSet, ci::CI{SVF,S}, set::S) where {S <: BOUNDS}
+function MOI.set(o::SCIP.Optimizer, ::MOI.ConstraintSet, ci::CI{VI,S}, set::S) where {S <: BOUNDS}
     allow_modification(o)
     v = var(o, VI(ci.value)) # cons index is actually var index
     lb, ub = bounds(set)
@@ -209,15 +218,28 @@ function MOI.set(o::SCIP.Optimizer, ::MOI.ConstraintSet, ci::CI{SVF,S}, set::S)
 end
 
 # TODO: is actually wrong for unbounded variables?
-function MOI.is_valid(o::Optimizer, ci::CI{SVF,<:BOUNDS})
-    return haskey(o.inner.vars, VarRef(ci.value))
+function MOI.is_valid(o::Optimizer, ci::CI{VI,S}) where {S <: BOUNDS}
+    if !haskey(o.inner.vars, VarRef(ci.value))
+        return false
+    end
+    cons_set = get(o.constypes, (VI, S), nothing)
+    if cons_set === nothing
+        return false
+    end
+    return ConsRef(ci.value) in o.constypes[VI, S]
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{SVF, S}) where S <: BOUNDS
-    return SVF(VI(ci.value))
+function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VI, S}) where {S <: BOUNDS}
+    if !MOI.is_valid(o, ci)
+        throw(MOI.InvalidIndex(ci))
+    end
+    return VI(ci.value)
 end
 
-function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{SVF, S}) where S <: BOUNDS
+function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{VI, S}) where {S <: BOUNDS}
+    if !MOI.is_valid(o, ci)
+        throw(MOI.InvalidIndex(ci))
+    end
     vi = VI(ci.value)
     v = var(o, vi)
     lb, ub = SCIPvarGetLbOriginal(v), SCIPvarGetUbOriginal(v)
@@ -228,6 +250,49 @@ function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{SVF, S}) where S <: B
     return from_bounds(S, lb, ub)
 end
 
+function MOI.is_valid(o::Optimizer, ci::CI{VI,S}) where {S <: Union{MOI.ZeroOne, MOI.Integer}}
+    if !haskey(o.inner.vars, VarRef(ci.value))
+        return false
+    end
+    return ConsRef(ci.value) in o.constypes[VI, S]
+end
+
+function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{VI, MOI.ZeroOne})
+    vi = VI(ci.value)
+    v = var(o, vi)
+    if SCIPvarGetType(v) == SCIP_VARTYPE_BINARY
+        return MOI.ZeroOne()
+    end
+    throw(MOI.InvalidIndex(ci))
+end
+
+function MOI.get(o::Optimizer, ::MOI.ConstraintSet, ci::CI{VI, MOI.Integer})
+    vi = VI(ci.value)
+    v = var(o, vi)
+    if SCIPvarGetType(v) == SCIP_VARTYPE_INTEGER
+        return MOI.Integer()
+    end
+    throw(MOI.InvalidIndex(ci))
+end
+
+function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VI, MOI.ZeroOne})
+    vi = VI(ci.value)
+    v = var(o, vi)
+    if SCIPvarGetType(v) == SCIP_VARTYPE_BINARY
+        return vi
+    end
+    throw(MOI.InvalidIndex(ci))
+end
+
+function MOI.get(o::Optimizer, ::MOI.ConstraintFunction, ci::CI{VI, MOI.Integer})
+    vi = VI(ci.value)
+    v = var(o, vi)
+    if SCIPvarGetType(v) == SCIP_VARTYPE_INTEGER
+        return vi
+    end
+    throw(MOI.InvalidIndex(ci))
+end
+
 # (partial) warm starts
 
 MOI.supports(::Optimizer, ::MOI.VariablePrimalStart, ::Type{VI}) = true
@@ -251,3 +316,7 @@ function MOI.set(o::Optimizer, ::MOI.VariablePrimalStart, vi::VI, value::Nothing
     end
     return
 end
+
+function MOI.set(::Optimizer, ::MOI.ConstraintFunction, ::CI{VI}, ::VI)
+    throw(MOI.SettingVariableIndexNotAllowed())
+end
diff --git a/test/MOI_additional.jl b/test/MOI_additional.jl
index cbe9135f..129fe460 100644
--- a/test/MOI_additional.jl
+++ b/test/MOI_additional.jl
@@ -3,204 +3,17 @@ const MOI = MathOptInterface
 
 const VI = MOI.VariableIndex
 const CI = MOI.ConstraintIndex
-const SVF = MOI.SingleVariable
 
 function var_bounds(o::SCIP.Optimizer, vi::VI)
-    return MOI.get(o, MOI.ConstraintSet(), CI{SVF,MOI.Interval{Float64}}(vi.value))
+    return MOI.get(o, MOI.ConstraintSet(), CI{VI,MOI.Interval{Float64}}(vi.value))
 end
 
 function chg_bounds(o::SCIP.Optimizer, vi::VI, set::S) where S
-    ci = CI{SVF,S}(vi.value)
+    ci = CI{VI,S}(vi.value)
     MOI.set(o, MOI.ConstraintSet(), ci, set)
     return nothing
 end
 
-@testset "Binary variables and explicit bounds" begin
-    optimizer = SCIP.Optimizer()
-
-    # Binary variable without explicit bounds.
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    @test_throws KeyError var_bounds(optimizer, x) == MOI.Interval(0.0, 1.0)
-
-    # Binary variable with [0, 1] bounds.
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(0.0, 1.0))
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 1.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 1.0)
-
-    # Binary variable with [0, 1] bounds (order should not matter).
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(0.0, 1.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 1.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 1.0)
-
-    # Binary variable fixed to 0.
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    b = MOI.add_constraint(optimizer, x, MOI.EqualTo(0.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 0.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 0.0)
-
-    # Binary variable fixed to 0 (different order).
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.EqualTo(0.0))
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 0.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(0.0, 0.0)
-
-    # Binary variable fixed to 1.
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    b = MOI.add_constraint(optimizer, x, MOI.EqualTo(1.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(1.0, 1.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(1.0, 1.0)
-
-    # Binary variable fixed to 1 (different order).
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.EqualTo(1.0))
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    @test var_bounds(optimizer, x) == MOI.Interval(1.0, 1.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(1.0, 1.0)
-
-    # Tightened bounds for binary variable
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(-1.0, 2.0))
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    @test var_bounds(optimizer, x) == MOI.Interval(-1.0, 2.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(-1.0, 2.0)
-
-    # Tightened bounds for binary variable (different order).
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(-1.0, 2.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(-1.0, 2.0)
-    MOI.delete(optimizer, t)
-    @test var_bounds(optimizer, x) == MOI.Interval(-1.0, 2.0)
-
-    # No error: binary variable with conflicting bounds (infeasible).
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(2.0, 3.0))
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, 3.0)
-
-    # No error: binary variable with conflicting bounds (infeasible, different order).
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    t = MOI.add_constraint(optimizer, x, MOI.ZeroOne())
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(2.0, 3.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, 3.0)
-end
-
-@testset "Bound constraints for a general variable." begin
-    optimizer = SCIP.Optimizer()
-    inf = SCIP.SCIPinfinity(optimizer)
-
-    # Should work: variable without explicit bounds
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    @test var_bounds(optimizer, x) == MOI.Interval(-inf, inf)
-
-    # Should work: variable with range bounds, but only once!
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(2.0, 3.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, 3.0)
-    @test_throws ErrorException MOI.add_constraint(optimizer, x, MOI.Interval(3.0, 4.0))
-
-    # Should work: variable with lower bound, but only once!
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.GreaterThan(2.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, inf)
-    @test_throws ErrorException MOI.add_constraint(optimizer, x, MOI.GreaterThan(3.0))
-
-    # Should work: variable with lower bound, but only once!
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.LessThan(2.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(-inf, 2.0)
-    @test_throws ErrorException MOI.add_constraint(optimizer, x, MOI.LessThan(3.0))
-
-    # Should work: fixed variable, but only once!
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.EqualTo(2.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, 2.0)
-    @test_throws ErrorException MOI.add_constraint(optimizer, x, MOI.EqualTo(3.0))
-
-    # Mixed constraint types now allowed (when disjoint)!
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    lb = MOI.add_constraint(optimizer, x, MOI.GreaterThan(2.0))
-    ub = MOI.add_constraint(optimizer, x, MOI.LessThan(3.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, 3.0)
-end
-
-@testset "Changing bounds for variable." begin
-    optimizer = SCIP.Optimizer()
-    inf = SCIP.SCIPinfinity(optimizer)
-
-    # change interval bounds
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.Interval(2.0, 3.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, 3.0)
-    chg_bounds(optimizer, x, MOI.Interval(4.0, 5.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(4.0, 5.0)
-
-    # change lower bound
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.GreaterThan(2.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, inf)
-    chg_bounds(optimizer, x, MOI.GreaterThan(4.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(4.0, inf)
-
-    # change upper bound
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.LessThan(3.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(-inf, 3.0)
-    chg_bounds(optimizer, x, MOI.LessThan(5.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(-inf, 5.0)
-
-    # change fixed value
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.EqualTo(2.5))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.5, 2.5)
-    chg_bounds(optimizer, x, MOI.EqualTo(4.5))
-    @test var_bounds(optimizer, x) == MOI.Interval(4.5, 4.5)
-
-    # change mixed
-    MOI.empty!(optimizer)
-    x = MOI.add_variable(optimizer)
-    b = MOI.add_constraint(optimizer, x, MOI.GreaterThan(2.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(2.0, inf)
-    chg_bounds(optimizer, x, MOI.LessThan(4.0))
-    @test var_bounds(optimizer, x) == MOI.Interval(-inf, 4.0)
-end
-
 @testset "Second Order Cone Constraint" begin
     # Derived from MOI's problem SOC1
     # max 0x + 1y + 1z
@@ -217,7 +30,7 @@ end
             MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.([1.0,1.0], [y,z]), 0.0))
     MOI.set(optimizer, MOI.ObjectiveSense(), MOI.MAX_SENSE)
 
-    ceq = MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.EqualTo(1.0))
+    ceq = MOI.add_constraint(optimizer, x, MOI.EqualTo(1.0))
     csoc = MOI.add_constraint(optimizer, MOI.VectorOfVariables([x, y, z]),
                               MOI.SecondOrderCone(3))
 
@@ -246,8 +59,8 @@ end
 
     x, y = MOI.add_variables(optimizer, 2)
 
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.Interval(0.0, 1.0))
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.GreaterThan(2.0))
+    MOI.add_constraint(optimizer, x, MOI.Interval(0.0, 1.0))
+    MOI.add_constraint(optimizer, y, MOI.GreaterThan(2.0))
     MOI.add_constraint(optimizer, MOI.VectorOfVariables([x, y]), MOI.SecondOrderCone(2))
 
     MOI.optimize!(optimizer)
@@ -261,7 +74,7 @@ end
     @test_throws ErrorException MOI.add_constraint(
         optimizer, MOI.VectorOfVariables([x, y]), MOI.SecondOrderCone(2))
 
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.GreaterThan(0.0))
+    MOI.add_constraint(optimizer, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(optimizer, MOI.VectorOfVariables([x, y]),
                        MOI.SecondOrderCone(2))
     # no error
@@ -271,9 +84,9 @@ end
     optimizer = SCIP.Optimizer(display_verblevel=0)
 
     x, y, z = MOI.add_variables(optimizer, 3)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.LessThan(1.0))
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.LessThan(1.0))
-    MOI.add_constraint(optimizer, MOI.SingleVariable(z), MOI.LessThan(1.0))
+    MOI.add_constraint(optimizer, x, MOI.LessThan(1.0))
+    MOI.add_constraint(optimizer, y, MOI.LessThan(1.0))
+    MOI.add_constraint(optimizer, z, MOI.LessThan(1.0))
 
     c = MOI.add_constraint(optimizer, MOI.VectorOfVariables([x,y,z]), MOI.SOS1([1.0,2.0,3.0]))
 
@@ -299,9 +112,9 @@ end
     optimizer = SCIP.Optimizer(display_verblevel=0)
 
     x, y, z = MOI.add_variables(optimizer, 3)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.LessThan(1.0))
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.LessThan(1.0))
-    MOI.add_constraint(optimizer, MOI.SingleVariable(z), MOI.LessThan(1.0))
+    MOI.add_constraint(optimizer, x, MOI.LessThan(1.0))
+    MOI.add_constraint(optimizer, y, MOI.LessThan(1.0))
+    MOI.add_constraint(optimizer, z, MOI.LessThan(1.0))
 
     c = MOI.add_constraint(optimizer, MOI.VectorOfVariables([x,y,z]), MOI.SOS2([1.0,2.0,3.0]))
 
@@ -332,8 +145,8 @@ end
     optimizer = SCIP.Optimizer(display_verblevel=0)
 
     x1, x2, z1, z2 = MOI.add_variables(optimizer, 4)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(z1), MOI.LessThan(4.0))
-    MOI.add_constraint(optimizer, MOI.SingleVariable(z2), MOI.GreaterThan(-8.0))
+    MOI.add_constraint(optimizer, z1, MOI.LessThan(4.0))
+    MOI.add_constraint(optimizer, z2, MOI.GreaterThan(-8.0))
 
     c1 = MOI.add_constraint(optimizer, MOI.VectorOfVariables([x1, z1]),
                             SCIP.AbsolutePowerSet(2.0))
@@ -369,7 +182,7 @@ end
     x3 = MOI.add_variable(optimizer)
     y  = MOI.add_variable(optimizer)
     t = MOI.add_constraint(optimizer, y, MOI.ZeroOne())
-    iset = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(1.0))
+    iset = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(1.0))
     ind_func = MOI.VectorAffineFunction(
         [MOI.VectorAffineTerm(1, MOI.ScalarAffineTerm(1.0, y)),
          MOI.VectorAffineTerm(2, MOI.ScalarAffineTerm(1.0, x1)),
@@ -428,10 +241,10 @@ end
 
     # Happy Path: add objective and retrieve it.
     x = MOI.add_variable(optimizer)
-    obj = MOI.SingleVariable(x)
-    MOI.set(optimizer, MOI.ObjectiveFunction{MOI.SingleVariable}(), obj)
+    obj = x
+    MOI.set(optimizer, MOI.ObjectiveFunction{MOI.VariableIndex}(), obj)
     MOI.set(optimizer, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-    @test MOI.get(optimizer, MOI.ObjectiveFunction{MOI.SingleVariable}()) == obj
+    @test MOI.get(optimizer, MOI.ObjectiveFunction{MOI.VariableIndex}()) == obj
     @test MOI.get(optimizer, MOI.ObjectiveSense()) == MOI.MAX_SENSE
     @test MOI.get(optimizer, MOI.ObjectiveFunctionType()) == MOI.ScalarAffineFunction{Float64}
 
@@ -443,33 +256,33 @@ end
     aff_obj = MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(1.0, x)], 3.0)
     MOI.set(optimizer, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(), aff_obj)
     MOI.set(optimizer, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-    @test_throws ErrorException MOI.get(optimizer, MOI.ObjectiveFunction{MOI.SingleVariable}())
+    @test_throws InexactError MOI.get(optimizer, MOI.ObjectiveFunction{MOI.VariableIndex}())
 end
 
 @testset "set_parameter" begin
     # bool
     optimizer = SCIP.Optimizer(branching_preferbinary=true)
-    @test MOI.get(optimizer, MOI.RawParameter("branching/preferbinary")) == true
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("branching/preferbinary")) == true
 
     # int
     optimizer = SCIP.Optimizer(conflict_minmaxvars=1)
-    @test MOI.get(optimizer, MOI.RawParameter("conflict/minmaxvars")) == 1
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("conflict/minmaxvars")) == 1
 
     # long int
     optimizer = SCIP.Optimizer(heuristics_alns_maxnodes=2)
-    @test MOI.get(optimizer, MOI.RawParameter("heuristics/alns/maxnodes")) == 2
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("heuristics/alns/maxnodes")) == 2
 
     # real
     optimizer = SCIP.Optimizer(branching_scorefac=0.15)
-    @test MOI.get(optimizer, MOI.RawParameter("branching/scorefac")) == 0.15
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("branching/scorefac")) == 0.15
 
     # char
     optimizer = SCIP.Optimizer(branching_scorefunc='s')
-    @test MOI.get(optimizer, MOI.RawParameter("branching/scorefunc")) == 's'
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("branching/scorefunc")) == 's'
 
     # string
     optimizer = SCIP.Optimizer(heuristics_alns_rewardfilename="abc.txt")
-    @test MOI.get(optimizer, MOI.RawParameter("heuristics/alns/rewardfilename")) == "abc.txt"
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("heuristics/alns/rewardfilename")) == "abc.txt"
 
     # invalid
     @test_throws ErrorException SCIP.Optimizer(some_invalid_param_name=true)
@@ -479,31 +292,31 @@ end
     optimizer = SCIP.Optimizer()
 
     # bool
-    MOI.set(optimizer, MOI.RawParameter("branching/preferbinary"), true)
-    @test MOI.get(optimizer, MOI.RawParameter("branching/preferbinary")) == true
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("branching/preferbinary"), true)
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("branching/preferbinary")) == true
 
     # int
-    MOI.set(optimizer, MOI.RawParameter("conflict/minmaxvars"), 1)
-    @test MOI.get(optimizer, MOI.RawParameter("conflict/minmaxvars")) == 1
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("conflict/minmaxvars"), 1)
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("conflict/minmaxvars")) == 1
 
     # long int
-    MOI.set(optimizer, MOI.RawParameter("heuristics/alns/maxnodes"), 2)
-    @test MOI.get(optimizer, MOI.RawParameter("heuristics/alns/maxnodes")) == 2
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("heuristics/alns/maxnodes"), 2)
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("heuristics/alns/maxnodes")) == 2
 
     # real
-    MOI.set(optimizer, MOI.RawParameter("branching/scorefac"), 0.15)
-    @test MOI.get(optimizer, MOI.RawParameter("branching/scorefac")) == 0.15
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("branching/scorefac"), 0.15)
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("branching/scorefac")) == 0.15
 
     # char
-    MOI.set(optimizer, MOI.RawParameter("branching/scorefunc"), 's')
-    @test MOI.get(optimizer, MOI.RawParameter("branching/scorefunc")) == 's'
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("branching/scorefunc"), 's')
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("branching/scorefunc")) == 's'
 
     # string
-    MOI.set(optimizer, MOI.RawParameter("heuristics/alns/rewardfilename"), "abc.txt")
-    @test MOI.get(optimizer, MOI.RawParameter("heuristics/alns/rewardfilename")) == "abc.txt"
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("heuristics/alns/rewardfilename"), "abc.txt")
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("heuristics/alns/rewardfilename")) == "abc.txt"
 
     # invalid
-    @test_throws ErrorException MOI.set(optimizer, MOI.RawParameter("some/invalid/param/name"), true)
+    @test_throws ErrorException MOI.set(optimizer, MOI.RawOptimizerAttribute("some/invalid/param/name"), true)
 end
 
 @testset "Silent" begin
@@ -513,17 +326,17 @@ end
 
     # "loud" by default
     @test MOI.get(optimizer, MOI.Silent()) == false
-    @test MOI.get(optimizer, MOI.RawParameter("display/verblevel")) == 4
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("display/verblevel")) == 4
 
     # make it silent
     MOI.set(optimizer, MOI.Silent(), true)
     @test MOI.get(optimizer, MOI.Silent()) == true
-    @test MOI.get(optimizer, MOI.RawParameter("display/verblevel")) == 0
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("display/verblevel")) == 0
 
     # but a user can override it
-    MOI.set(optimizer, MOI.RawParameter("display/verblevel"), 1)
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("display/verblevel"), 1)
     @test MOI.get(optimizer, MOI.Silent()) == false
-    @test MOI.get(optimizer, MOI.RawParameter("display/verblevel")) == 1
+    @test MOI.get(optimizer, MOI.RawOptimizerAttribute("display/verblevel")) == 1
 end
 
 @testset "Query results (before/after solve)" begin
@@ -531,8 +344,8 @@ end
     atol, rtol = 1e-6, 1e-6
 
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.GreaterThan(0.0))
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.GreaterThan(0.0))
+    MOI.add_constraint(optimizer, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint(optimizer, y, MOI.GreaterThan(0.0))
 
     c = MOI.add_constraint(
         optimizer,
@@ -552,7 +365,7 @@ end
     @test_throws ErrorException MOI.get(optimizer, MOI.ConstraintPrimal(), c)
     @test_throws ErrorException MOI.get(optimizer, MOI.ObjectiveBound())
     @test_throws ErrorException MOI.get(optimizer, MOI.RelativeGap())
-    @test MOI.get(optimizer, MOI.SolveTime()) ≈ 0.0 atol=atol rtol=rtol
+    @test MOI.get(optimizer, MOI.SolveTimeSec()) ≈ 0.0 atol=atol rtol=rtol
     @test_throws ErrorException MOI.get(optimizer, MOI.SimplexIterations())
     @test MOI.get(optimizer, MOI.NodeCount()) == 0
 
@@ -567,7 +380,7 @@ end
     @test MOI.get(optimizer, MOI.ConstraintPrimal(), c) ≈ 1.0 atol=atol rtol=rtol
     @test MOI.get(optimizer, MOI.ObjectiveBound()) ≈ 2.0 atol=atol rtol=rtol
     @test MOI.get(optimizer, MOI.RelativeGap()) ≈ 0.0 atol=atol rtol=rtol
-    @test MOI.get(optimizer, MOI.SolveTime()) < 1.0
+    @test MOI.get(optimizer, MOI.SolveTimeSec()) < 1.0
     @test MOI.get(optimizer, MOI.SimplexIterations()) <= 3  # conservative
     @test MOI.get(optimizer, MOI.NodeCount()) <= 1          # conservative
 end
diff --git a/test/MOI_conshdlr.jl b/test/MOI_conshdlr.jl
index 2b1c78f5..1cc93a32 100644
--- a/test/MOI_conshdlr.jl
+++ b/test/MOI_conshdlr.jl
@@ -7,8 +7,8 @@ const MOI = MathOptInterface
 
     # add two binary variables: x, y
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # maximize 2x + y
     MOI.set(optimizer, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
@@ -38,9 +38,9 @@ end
 
     # add three binary variables
     x, y, z = MOI.add_variables(optimizer, 3)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(z), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, z, MOI.ZeroOne())
 
     # maximize 2x + 3y + 2z
     MOI.set(optimizer, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
@@ -72,9 +72,9 @@ end
 
     # add three binary variables
     x, y, z = MOI.add_variables(optimizer, 3)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(z), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, z, MOI.ZeroOne())
 
     # maximize 2x + 3y + 2z
     MOI.set(optimizer, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
@@ -104,9 +104,9 @@ end
 
     # add three binary variables
     x, y, z = MOI.add_variables(optimizer, 3)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(z), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, z, MOI.ZeroOne())
 
     # maximize 2x + 3y + 2z
     MOI.set(optimizer, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
@@ -135,8 +135,8 @@ end
     # add three integer variables, in {0, 1, 2}
     x, y, z = MOI.add_variables(optimizer, 3)
     for v in [x, y, z]
-        MOI.add_constraint(optimizer, MOI.SingleVariable(v), MOI.Integer())
-        MOI.add_constraint(optimizer, MOI.SingleVariable(v), MOI.Interval(0.0, 2.0))
+        MOI.add_constraint(optimizer, v, MOI.Integer())
+        MOI.add_constraint(optimizer, v, MOI.Interval(0.0, 2.0))
     end
 
     # maximize 2x + y
@@ -166,9 +166,9 @@ end
     optimizer = SCIP.Optimizer(display_verblevel=0, presolving_maxrounds=0)
 
     allow_dual_reductions = if SCIP.SCIPmajorVersion() < 7
-        MOI.RawParameter("misc/allowdualreds")
+        MOI.RawOptimizerAttribute("misc/allowdualreds")
     else
-        MOI.RawParameter("misc/allowstrongdualreds")
+        MOI.RawOptimizerAttribute("misc/allowstrongdualreds")
     end
     MOI.set(optimizer, allow_dual_reductions, SCIP.FALSE)
 
@@ -176,8 +176,8 @@ end
 
     # add binary variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # maximize 2x + y
     MOI.set(optimizer, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}(),
diff --git a/test/MOI_nonlinear_exprs.jl b/test/MOI_nonlinear_exprs.jl
index b8607543..ba27ef93 100644
--- a/test/MOI_nonlinear_exprs.jl
+++ b/test/MOI_nonlinear_exprs.jl
@@ -118,7 +118,7 @@ end
 
 @testset "add nonlinear constraint after solve" begin
     optimizer = SCIP.Optimizer()
-    MOI.set(optimizer, MOI.RawParameter("display/verblevel"), 0)
+    MOI.set(optimizer, MOI.RawOptimizerAttribute("display/verblevel"), 0)
 
     x, y = MOI.add_variables(optimizer, 2)
 
diff --git a/test/MOI_wrapper_bridged.jl b/test/MOI_wrapper_bridged.jl
index ee653a8b..e441bfb8 100644
--- a/test/MOI_wrapper_bridged.jl
+++ b/test/MOI_wrapper_bridged.jl
@@ -4,60 +4,21 @@ const MOIB = MOI.Bridges
 const MOIT = MOI.Test
 
 const BRIDGED = MOIB.full_bridge_optimizer(SCIP.Optimizer(display_verblevel=0), Float64)
-const CONFIG = MOIT.TestConfig(atol=1e-5, rtol=1e-5, duals=false, infeas_certificates=false)
-const CONFIG3 = MOIT.TestConfig(atol=1e-3, rtol=1e-2, duals=false, infeas_certificates=false)
-
-@testset "MOI Continuous Linear" begin
-    excluded = [
-        "linear1",  # needs MOI.delete (of variables in constraints)
-        "linear5",  # needs MOI.delete (of variables in constraints)
-        "linear11", # broken in SCIP (#2556)
-        "linear13", # TODO: support MOI.FEASIBILITY_SENSE
-        "linear14", # needs MOI.delete (of variables in constraints)
-    ]
-    MOIT.contlineartest(BRIDGED, CONFIG, excluded)
-end
-
-@testset "MOI Continuous Conic" begin
-    MOIT.lintest(BRIDGED, CONFIG)
-
-    # SOC tests fail because of lower bound requirement of RHS var.
-    # MOIT.soctest(BRIDGED, CONFIG)
-    # MOIT.rsoctest(BRIDGED, CONFIG)
-
-    # other cones not supported
-    # MOIT.geomeantest(BRIDGED, CONFIG)
-    # MOIT.exptest(BRIDGED, CONFIG)
-    # MOIT.sdptest(BRIDGED, CONFIG)
-    # MOIT.logdettest(BRIDGED, CONFIG)
-    # MOIT.rootdettest(BRIDGED, CONFIG)
-end
-
-@testset "MOI Quadratic Constraint" begin
-    # needs objective bridge (MOI/#529)
-    # MOIT.qptest(BRIDGED, CONFIG)
-
-    MOIT.qcptest(BRIDGED, CONFIG)
-    MOIT.socptest(BRIDGED, CONFIG3)
-end
-
-@testset "MOI Integer Linear" begin
-    excluded = String["semiconttest", "semiinttest"]
-    MOIT.intlineartest(BRIDGED, CONFIG, excluded)
-    MOIT.indicator3_test(BRIDGED, CONFIG)
-end
-
-@testset "MOI Integer Conic" begin
-    # SOC tests fail because of lower bound requirement of RHS var.
-    # MOIT.intconictest(BRIDGED, CONFIG)
-end
-
-@testset "MOI NLP" begin
-    # None of tests provide expression graphs in the evaluator.
-    # MOIT.nlptest(BRIDGED, CONFIG)
-end
-
-@testset "MOI Unit tests" begin
-    # TODO: most tests need get-variable-by-name etc.
-    # MOIT.unittest(BRIDGED, CONFIG)
+const CONFIG_BRIDGED = MOIT.Config(atol=1e-5, rtol=1e-5, exclude=Any[
+    MOI.ConstraintDual, MOI.ConstraintName, MOI.VariableName, MOI.DualObjectiveValue, MOI.VariableBasisStatus, MOI.ConstraintBasisStatus,
+])
+
+@testset "MOI unit tests" begin
+    excluded = copy(MOI_BASE_EXCLUDED)
+    append!(excluded, [
+        "test_linear_integration", # Can not delete variable while model contains constraints
+        "test_quadratic_duplicate_terms", # Can not delete variable while model contains constraints
+        "test_quadratic_nonhomogeneous", # unsupported by bridge
+    ])
+    MOIT.runtests(
+        BRIDGED,
+        CONFIG_BRIDGED,
+        warn_unsupported=false,
+        exclude = excluded,
+    )
 end
diff --git a/test/MOI_wrapper_cached.jl b/test/MOI_wrapper_cached.jl
index a0c148ea..195d8469 100644
--- a/test/MOI_wrapper_cached.jl
+++ b/test/MOI_wrapper_cached.jl
@@ -17,19 +17,25 @@ const CACHE = MOIU.UniversalFallback(ModelData{Float64}())
 const CACHED = MOIU.CachingOptimizer(CACHE, SCIP.Optimizer(display_verblevel=0))
 const BRIDGED2 = MOIB.full_bridge_optimizer(CACHED, Float64)
 
-const CONFIG = MOIT.TestConfig(atol=1e-5, rtol=1e-5, duals=false, infeas_certificates=false)
-const CONFIG3 = MOIT.TestConfig(atol=1e-3, rtol=1e-2, duals=false, infeas_certificates=false)
-
-@testset "MOI Unit tests" begin
-    excluded = [
-        "feasibility_sense", # TODO: support feasibility sense
-        "solve_qp_edge_cases", # needs objective bridge
-        "number_threads", # can't set num. threads in single-threaded SCIP!
-        "delete_soc_variables", # SCIP requires non-negative "rhs variable"
-    ]
-    MOIT.unittest(BRIDGED2, CONFIG, excluded)
-end
+const CONFIG_CACHED = MOIT.Config(
+    atol=1e-5, rtol=1e-5,
+    exclude=Any[
+        MOI.ConstraintDual, MOI.ConstraintName, MOI.VariableName, MOI.DualObjectiveValue, MOI.VariableBasisStatus, MOI.ConstraintBasisStatus,
+    ],
+)
 
 @testset "MOI Modification tests" begin
-    MOIT.modificationtest(BRIDGED2, CONFIG)
+    exclude_list = copy(MOI_BASE_EXCLUDED)
+    append!(
+        exclude_list,
+        [
+            "RawStatusString",
+            "SolveTimeSec",
+            "test_conic_",
+            "test_linear_integration",
+            "test_quadratic_duplicate_terms",
+            "test_quadratic_nonhomogeneous",
+        ]
+    )
+    MOIT.runtests(BRIDGED2, CONFIG_CACHED, exclude = exclude_list)
 end
diff --git a/test/MOI_wrapper_direct.jl b/test/MOI_wrapper_direct.jl
index 2d74bd0c..371cf620 100644
--- a/test/MOI_wrapper_direct.jl
+++ b/test/MOI_wrapper_direct.jl
@@ -3,51 +3,25 @@ const MOI = MathOptInterface
 const MOIT = MOI.Test
 
 const OPTIMIZER = SCIP.Optimizer(display_verblevel=0)
-const CONFIG = MOIT.TestConfig(atol=1e-5, rtol=1e-5, duals=false,
-                               infeas_certificates=false)
-
-@testset "MOI Continuous Linear" begin
-    # remember reason for excluded tests:
-    excluded = [
-        "linear1",  # needs MOI.delete (of variables in constraints)
-        "linear5",  # needs MOI.delete (of variables in constraints)
-        "linear7",  # needs MOI.VectorAffineFunction
-        "linear11", # broken in SCIP (#2556)
-        "linear13", # TODO: support MOI.FEASIBILITY_SENSE
-        "linear14", # needs MOI.delete (of variables in constraints)
-        "linear15", # needs MOI.VectorAffineFunction
-    ]
-    # MOIT.contlineartest(OPTIMIZER, CONFIG, excluded)
-
-    # call individual tests
-    MOIT.linear2test(OPTIMIZER, CONFIG)
-    MOIT.linear3test(OPTIMIZER, CONFIG)
-    MOIT.linear4test(OPTIMIZER, CONFIG)
-    MOIT.linear6test(OPTIMIZER, CONFIG)
-    MOIT.linear8atest(OPTIMIZER, CONFIG)
-    MOIT.linear8btest(OPTIMIZER, CONFIG)
-    MOIT.linear8ctest(OPTIMIZER, CONFIG)
-    MOIT.linear9test(OPTIMIZER, CONFIG)
-    MOIT.linear10test(OPTIMIZER, CONFIG)
-    MOIT.linear10btest(OPTIMIZER, CONFIG)
-    MOIT.linear12test(OPTIMIZER, CONFIG)
-    MOIT.partial_start_test(OPTIMIZER, CONFIG)
-end
-
-@testset "MOI Quadratic Constraint" begin
-    # remember reason for excluded tests:
-    excluded = [
-        "qcp1", # needs VectorAffineFunction
-    ]
-    # MOIT.qcptest(OPTIMIZER, CONFIG, excluded)
-
-    # call individual tests
-    MOIT.qcp2test(OPTIMIZER, CONFIG)
-    MOIT.qcp3test(OPTIMIZER, CONFIG)
-    MOIT.qcp4test(OPTIMIZER, CONFIG)
+const CONFIG_DIRECT = MOIT.Config(
+    atol=1e-5, rtol=1e-5,
+    exclude=Any[
+        MOI.ConstraintDual, MOI.ConstraintName, MOI.VariableName, MOI.DualObjectiveValue, MOI.VariableBasisStatus, MOI.ConstraintBasisStatus,
+    ],
+)
+
+@testset "MOI unit tests" begin
+    excluded = copy(MOI_BASE_EXCLUDED)
+    append!(excluded, [
+            "test_linear_integration", # Can not delete variable while model contains constraints
+    ])
+    MOIT.runtests(
+        OPTIMIZER,
+        CONFIG_DIRECT,
+        warn_unsupported=false,
+        exclude = excluded,
+    )
 
-    MOIT.ncqcp1test(OPTIMIZER, CONFIG)
-    MOIT.ncqcp2test(OPTIMIZER, CONFIG)
 end
 
 function indicator4_test(model::MOI.ModelLike, config)
@@ -67,10 +41,10 @@ function indicator4_test(model::MOI.ModelLike, config)
 
     @test MOI.supports(model, MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}())
     @test MOI.supports(model, MOI.ObjectiveSense())
-    @test MOI.supports_constraint(model, MOI.SingleVariable, MOI.ZeroOne)
-    @test MOI.supports_constraint(model, MOI.SingleVariable, MOI.Interval{Float64})
+    @test MOI.supports_constraint(model, MOI.VariableIndex, MOI.ZeroOne)
+    @test MOI.supports_constraint(model, MOI.VariableIndex, MOI.Interval{Float64})
     @test MOI.supports_constraint(model, MOI.ScalarAffineFunction{Float64}, MOI.Interval{Float64})
-    @test MOI.supports_constraint(model, MOI.VectorAffineFunction{Float64}, MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE, MOI.LessThan{Float64}})
+    @test MOI.supports_constraint(model, MOI.VectorAffineFunction{Float64}, MOI.Indicator{MOI.ACTIVATE_ON_ONE, MOI.LessThan{Float64}})
     x1 = MOI.add_variable(model)
     x2 = MOI.add_variable(model)
     z1 = MOI.add_variable(model)
@@ -83,7 +57,7 @@ function indicator4_test(model::MOI.ModelLike, config)
         ],
         [0.0, -1.0]
     )
-    iset1 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(7.0))
+    iset1 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(7.0))
     MOI.add_constraint(model, f1, iset1)
 
     f2 = MOI.VectorAffineFunction(
@@ -93,7 +67,7 @@ function indicator4_test(model::MOI.ModelLike, config)
         ],
         [0.0, 1.0],
     )
-    iset2 = MOI.IndicatorSet{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(10.0))
+    iset2 = MOI.Indicator{MOI.ACTIVATE_ON_ONE}(MOI.LessThan(10.0))
 
     MOI.add_constraint(model, f2, iset2)
 
@@ -114,32 +88,20 @@ function indicator4_test(model::MOI.ModelLike, config)
     )
     MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
 
-    if config.solve
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
+    @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
 
-        MOI.optimize!(model)
+    MOI.optimize!(model)
 
-        @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
-        @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
-        @test MOI.get(model, MOI.ObjectiveValue()) ≈ 28.75 atol=atol rtol=rtol
-        @test MOI.get(model, MOI.VariablePrimal(), x1) ≈ 1.25 atol=atol rtol=rtol
-        @test MOI.get(model, MOI.VariablePrimal(), x2) ≈ 8.75 atol=atol rtol=rtol
-        @test MOI.get(model, MOI.VariablePrimal(), z1) ≈ 0.0 atol=atol rtol=rtol
-        @test MOI.get(model, MOI.VariablePrimal(), z2) ≈ 1.0 atol=atol rtol=rtol
-    end
+    @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
+    @test MOI.get(model, MOI.PrimalStatus()) == MOI.FEASIBLE_POINT
+    @test MOI.get(model, MOI.ObjectiveValue()) ≈ 28.75 atol=atol rtol=rtol
+    @test MOI.get(model, MOI.VariablePrimal(), x1) ≈ 1.25 atol=atol rtol=rtol
+    @test MOI.get(model, MOI.VariablePrimal(), x2) ≈ 8.75 atol=atol rtol=rtol
+    @test MOI.get(model, MOI.VariablePrimal(), z1) ≈ 0.0 atol=atol rtol=rtol
+    @test MOI.get(model, MOI.VariablePrimal(), z2) ≈ 1.0 atol=atol rtol=rtol
 end
 
 @testset "MOI Integer Linear" begin
-    # MOIT.intlineartest(OPTIMIZER, CONFIG)
-
-    # call individual tests
-    MOIT.knapsacktest(OPTIMIZER, CONFIG)
-    MOIT.int1test(OPTIMIZER, CONFIG)
-    MOIT.int2test(OPTIMIZER, CONFIG)
-    MOIT.int3test(OPTIMIZER, CONFIG)
-    MOIT.indicator1_test(OPTIMIZER, CONFIG)
-    MOIT.indicator2_test(OPTIMIZER, CONFIG)
     # replace with MOIT when MathOptInterface.jl#929 merged
-    indicator4_test(OPTIMIZER, CONFIG)
-    # MOIT.indicator3_test(OPTIMIZER, CONFIG) # no support for ACTIVATE_ON_ZERO
+    indicator4_test(OPTIMIZER, CONFIG_DIRECT)
 end
diff --git a/test/cutcallback.jl b/test/cutcallback.jl
index 6d270eba..632bd9a5 100644
--- a/test/cutcallback.jl
+++ b/test/cutcallback.jl
@@ -14,8 +14,8 @@ const MOI = MathOptInterface
 
     # add variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # add constraint: x + y ≤ 1.5
     MOI.add_constraint(optimizer,
@@ -69,8 +69,8 @@ end
 
     # add variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # add constraint: x + y ≤ 1.5
     MOI.add_constraint(optimizer,
@@ -120,8 +120,8 @@ end
 
     # add variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # add constraint: x + y ≤ 1.5
     MOI.add_constraint(optimizer,
diff --git a/test/runtests.jl b/test/runtests.jl
index e8c29e1e..3dcf375d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -28,6 +28,55 @@ else
     @info "Separation and callbacks not tested for SCIP versions below 7"
 end
 
+const MOI_BASE_EXCLUDED = [
+    "Semicontinuous",
+    "ScalarAffineFunction_Semiinteger",
+    "ScalarAffineFunction_ZeroOne",
+    "ScalarQuadraticFunction_Semiinteger",
+    "ScalarQuadraticFunction_ZeroOne",
+    "VectorAffineFunction_GeometricMeanCone",
+    "Indicator_GreaterThan",
+    "Indicator_LessThan",
+    "VectorAffineFunction_NormOneCone",
+    "VectorQuadraticFunction_NormOneCone",
+    "VectorAffineFunction_RotatedSecondOrderCone", # SOC tests fail because of lower bound requirement of RHS var.
+    "VectorAffineFunction_SOS",
+    "VectorQuadraticFunction_SOS",
+    "VectorAffineFunction_SecondOrderCone",
+    "GeometricMeanCone",
+    "RotatedSecondOrderCone",
+    "SecondOrderCone",
+    "Indicator_ACTIVATE_ON_ZERO",
+    "test_constraint_ZeroOne_bounds", # accessing variable from string name
+    "test_constraint_get_ConstraintIndex",
+    "test_model_ListOfConstraintAttributesSet",
+    "BoundAlreadySet", # see TODO,
+    "ListOfConstraintIndices", # MathOptInterface.ListOfModelAttributesSet
+    "ListOfConstraintTypesPresent",
+    "ScalarAffineFunction_ConstraintName", # get(::SCIP.Optimizer, ::Type{MathOptInterface.ConstraintIndex}, ::String)
+    "ScalarFunctionConstantNotZero",
+    "UnsupportedAttribute",    # test_model_copy_to_UnsupportedAttribute: MOI.copy_to(model, BadVariableAttributeModel())
+    "UnsupportedConstraint",
+    "test_model_delete", # MOI.ListOfConstraintTypesPresent
+    "duplicate_VariableName", # get variable by name
+    "test_modification_coef_scalaraffine_",
+    "test_modification_coef_vectoraffine_",
+    "test_modification_const_vectoraffine_nonpos",
+    "test_modification_delete_variables_in_a_batch",
+    "test_modification_func_scalaraffine_",
+    "test_modification_func_vectoraffine_",
+    "test_modification_set_function_single_variable",
+    "test_modification_set_scalaraffine_",
+    "test_modification_set_singlevariable_",
+    "test_modification_transform_",
+    "test_nonlinear_", # None of tests provide expression graphs in the evaluator.
+    "FEASIBILITY_SENSE", # TODO
+    "ObjectiveFunction_ScalarAffineFunction",
+    "test_objective_set_via_modify",
+    "test_solve_ObjectiveBound_MAX_SENSE",
+    "test_solve_ObjectiveBound_MIN_SENSE",
+]
+
 @testset "MathOptInterface tests (bridged)" begin
     include("MOI_wrapper_bridged.jl")
 end
diff --git a/test/sepa.jl b/test/sepa.jl
index f2a9285b..853d8388 100644
--- a/test/sepa.jl
+++ b/test/sepa.jl
@@ -10,8 +10,8 @@ const MOI = MathOptInterface
 
     # add variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # add constraint: x + y ≤ 1.5
     MOI.add_constraint(optimizer,
@@ -50,8 +50,8 @@ end
 
     # add variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # add constraint: x + y ≤ 1.5
     MOI.add_constraint(optimizer,
@@ -97,8 +97,8 @@ end
 
     # add variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # add constraint: x + y ≤ 1.5
     MOI.add_constraint(optimizer,
@@ -144,8 +144,8 @@ end
 
     # add variables
     x, y = MOI.add_variables(optimizer, 2)
-    MOI.add_constraint(optimizer, MOI.SingleVariable(x), MOI.ZeroOne())
-    MOI.add_constraint(optimizer, MOI.SingleVariable(y), MOI.ZeroOne())
+    MOI.add_constraint(optimizer, x, MOI.ZeroOne())
+    MOI.add_constraint(optimizer, y, MOI.ZeroOne())
 
     # add constraint: x + y ≤ 1.5
     MOI.add_constraint(optimizer,