diff --git a/Project.toml b/Project.toml
index c90fc1443..e73dec2f2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRules"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "0.8.1"
+version = "0.8.2"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/rulesets/LinearAlgebra/dense.jl b/src/rulesets/LinearAlgebra/dense.jl
index 30769eca3..3145123a4 100644
--- a/src/rulesets/LinearAlgebra/dense.jl
+++ b/src/rulesets/LinearAlgebra/dense.jl
@@ -194,10 +194,19 @@ function frule((_, ΔA), ::typeof(pinv), A::AbstractMatrix{T}; kwargs...) where
     return Y, ∂Y
 end
 
+function rrule(
+    ::typeof(pinv),
+    x::Union{AbstractVector{T}, LinearAlgebra.AdjOrTransAbsVec{T}},
+) where {T<:Union{Real,Complex}}
+    y, full_pb = rrule(pinv, x, 0)
+    pinv_pullback(Δy) = return full_pb(Δy)[1:2]
+    return y, pinv_pullback
+end
+
 function rrule(
     ::typeof(pinv),
     x::AbstractVector{T},
-    tol::Real = 0,
+    tol::Real,
 ) where {T<:Union{Real,Complex}}
     y = pinv(x, tol)
     function pinv_pullback(Δy)
@@ -210,7 +219,7 @@ end
 function rrule(
     ::typeof(pinv),
     x::LinearAlgebra.AdjOrTransAbsVec{T},
-    tol::Real = 0,
+    tol::Real,
 ) where {T<:Union{Real,Complex}}
     y = pinv(x, tol)
     function pinv_pullback(Δy)
diff --git a/src/rulesets/LinearAlgebra/factorization.jl b/src/rulesets/LinearAlgebra/factorization.jl
index 109b16f80..9bb0f64de 100644
--- a/src/rulesets/LinearAlgebra/factorization.jl
+++ b/src/rulesets/LinearAlgebra/factorization.jl
@@ -428,8 +428,12 @@ end
 #####
 ##### `cholesky`
 #####
-
-function rrule(::typeof(cholesky), A::Real, uplo::Symbol=:U)
+function rrule(::typeof(cholesky), A::Real)
+    C, full_pb = rrule(cholesky, A, :U)
+    cholesky_pullback(ΔC::Tangent) = return full_pb(ΔC)[1:2]
+    return C, cholesky_pullback
+end
+function rrule(::typeof(cholesky), A::Real, uplo::Symbol)
     C = cholesky(A, uplo)
     function cholesky_pullback(ΔC::Tangent)
         return NoTangent(), ΔC.factors[1, 1] / (2 * C.U[1, 1]), NoTangent()
diff --git a/test/rulesets/LinearAlgebra/dense.jl b/test/rulesets/LinearAlgebra/dense.jl
index 2e70338b4..511e01aeb 100644
--- a/test/rulesets/LinearAlgebra/dense.jl
+++ b/test/rulesets/LinearAlgebra/dense.jl
@@ -50,7 +50,8 @@
 
         @testset "$F{Vector{$T}}" for T in (Float64, ComplexF64), F in (Transpose, Adjoint)
             test_frule(pinv, F(randn(T, 3)) ⊢ F(randn(T, 3)))
-            test_rrule(pinv, F(randn(T, 3)))
+            check_inferred = VERSION ≥ v"1.5"
+            test_rrule(pinv, F(randn(T, 3)); check_inferred=check_inferred)
 
             # Check types.
             # TODO: Do we need this still?
diff --git a/test/rulesets/LinearAlgebra/factorization.jl b/test/rulesets/LinearAlgebra/factorization.jl
index 397f1622f..534c45be4 100644
--- a/test/rulesets/LinearAlgebra/factorization.jl
+++ b/test/rulesets/LinearAlgebra/factorization.jl
@@ -357,7 +357,8 @@ end
     # also we might be missing some overloads for different tangent-types in the rules
     @testset "cholesky" begin
         @testset "Real" begin
-            test_rrule(cholesky, 0.8)
+            check_inferred = VERSION ≥ v"1.5"
+            test_rrule(cholesky, 0.8; check_inferred=check_inferred)
         end
         @testset "Diagonal{<:Real}" begin
             D = Diagonal(rand(5) .+ 0.1)