diff --git a/src/callbacks_step/alive.jl b/src/callbacks_step/alive.jl
index 9df7181521..9700f7e4cd 100644
--- a/src/callbacks_step/alive.jl
+++ b/src/callbacks_step/alive.jl
@@ -68,7 +68,6 @@ function (alive_callback::AliveCallback)(u, t, integrator)
     # We need to check the number of accepted steps since callbacks are not
     # activated after a rejected step.
     return alive_interval > 0 && ((integrator.stats.naccept % alive_interval == 0 &&
-             !(integrator.stats.naccept == 0 && integrator.iter > 0) &&
              (analysis_interval == 0 ||
               integrator.stats.naccept % analysis_interval != 0)) ||
             isfinished(integrator))
diff --git a/src/callbacks_step/analysis.jl b/src/callbacks_step/analysis.jl
index 8f89af755a..7b4a97c2a7 100644
--- a/src/callbacks_step/analysis.jl
+++ b/src/callbacks_step/analysis.jl
@@ -26,8 +26,8 @@ or `extra_analysis_errors = (:conservation_error,)`.
 If you want to omit the computation (to safe compute-time) of the [`default_analysis_errors`](@ref), specify
 `analysis_errors = Symbol[]`.
 Note: `default_analysis_errors` are `:l2_error` and `:linf_error` for all equations.
-If you want to compute `extra_analysis_errors` such as `:conservation_error` solely, i.e., 
-without `:l2_error, :linf_error` you need to specify 
+If you want to compute `extra_analysis_errors` such as `:conservation_error` solely, i.e.,
+without `:l2_error, :linf_error` you need to specify
 `analysis_errors = [:conservation_error]` instead of `extra_analysis_errors = [:conservation_error]`.
 
 Further scalar functions `func` in `extra_analysis_integrals` are applied to the numerical
@@ -119,9 +119,7 @@ function AnalysisCallback(mesh, equations::AbstractEquations, solver, cache;
     # We need to check the number of accepted steps since callbacks are not
     # activated after a rejected step.
     condition = (u, t, integrator) -> interval > 0 &&
-        ((integrator.stats.naccept % interval == 0 &&
-          !(integrator.stats.naccept == 0 && integrator.iter > 0)) ||
-         isfinished(integrator))
+        (integrator.stats.naccept % interval == 0 || isfinished(integrator))
 
     analyzer = SolutionAnalyzer(solver; kwargs...)
     cache_analysis = create_cache_analysis(analyzer, mesh, equations, solver, cache,
@@ -696,7 +694,7 @@ include("analysis_dg3d_parallel.jl")
 
 # Special analyze for `SemidiscretizationHyperbolicParabolic` such that
 # precomputed gradients are available. Required for `enstrophy` (see above) and viscous forces.
-# Note that this needs to be included after `analysis_surface_integral_2d.jl` to 
+# Note that this needs to be included after `analysis_surface_integral_2d.jl` to
 # have `VariableViscous` available.
 function analyze(quantity::AnalysisSurfaceIntegral{Variable},
                  du, u, t,
diff --git a/src/callbacks_step/save_restart.jl b/src/callbacks_step/save_restart.jl
index 0d174d8580..0b0d2420c7 100644
--- a/src/callbacks_step/save_restart.jl
+++ b/src/callbacks_step/save_restart.jl
@@ -83,8 +83,7 @@ function (restart_callback::SaveRestartCallback)(u, t, integrator)
     #    (total #steps)       (#accepted steps)
     # We need to check the number of accepted steps since callbacks are not
     # activated after a rejected step.
-    return interval > 0 && (((integrator.stats.naccept % interval == 0) &&
-             !(integrator.stats.naccept == 0 && integrator.iter > 0)) ||
+    return interval > 0 && (integrator.stats.naccept % interval == 0 ||
             (save_final_restart && isfinished(integrator)))
 end
 
@@ -198,7 +197,7 @@ function load_adaptive_time_integrator!(integrator, restart_file::AbstractString
         # Reevaluate integrator.fsal_first on the first step
         integrator.reeval_fsal = true
         # Load additional parameters for PIDController
-        if hasproperty(controller, :err) # Distinguish PIDController from PIController 
+        if hasproperty(controller, :err) # Distinguish PIDController from PIController
             controller.err[:] = read(attributes(file)["time_integrator_controller_err"])
         end
     end
diff --git a/src/callbacks_step/save_solution.jl b/src/callbacks_step/save_solution.jl
index c106fe69bc..870cea0b9f 100644
--- a/src/callbacks_step/save_solution.jl
+++ b/src/callbacks_step/save_solution.jl
@@ -174,8 +174,7 @@ function (solution_callback::SaveSolutionCallback)(u, t, integrator)
     #    (total #steps)       (#accepted steps)
     # We need to check the number of accepted steps since callbacks are not
     # activated after a rejected step.
-    return interval_or_dt > 0 && (((integrator.stats.naccept % interval_or_dt == 0) &&
-             !(integrator.stats.naccept == 0 && integrator.iter > 0)) ||
+    return interval_or_dt > 0 && (integrator.stats.naccept % interval_or_dt == 0 ||
             (save_final_solution && isfinished(integrator)))
 end
 
diff --git a/src/callbacks_step/visualization.jl b/src/callbacks_step/visualization.jl
index 98c0126a30..30ac88e9fd 100644
--- a/src/callbacks_step/visualization.jl
+++ b/src/callbacks_step/visualization.jl
@@ -137,8 +137,7 @@ function (visualization_callback::VisualizationCallback)(u, t, integrator)
     #    (total #steps)       (#accepted steps)
     # We need to check the number of accepted steps since callbacks are not
     # activated after a rejected step.
-    return interval > 0 && ((integrator.stats.naccept % interval == 0 &&
-             !(integrator.stats.naccept == 0 && integrator.iter > 0)) ||
+    return interval > 0 && (integrator.stats.naccept % interval == 0 ||
             isfinished(integrator))
 end