diff --git a/examples/1d/elixir_euler_sedov_blast_wave.jl b/examples/1d/elixir_euler_sedov_blast_wave.jl
index 354987c849..33d24c431c 100644
--- a/examples/1d/elixir_euler_sedov_blast_wave.jl
+++ b/examples/1d/elixir_euler_sedov_blast_wave.jl
@@ -54,7 +54,7 @@ amr_callback = AMRCallback(semi, amr_controller,
 
 summary_callback = SummaryCallback()
 
-stepsize_callback = StepsizeCallback(cfl=0.8)
+stepsize_callback = StepsizeCallback(cfl=0.5)
 
 save_solution = SaveSolutionCallback(interval=100,
                                      save_initial_solution=true,
diff --git a/test/test_examples_1d_euler.jl b/test/test_examples_1d_euler.jl
index 98c3e34188..91b065b67f 100644
--- a/test/test_examples_1d_euler.jl
+++ b/test/test_examples_1d_euler.jl
@@ -82,23 +82,24 @@ EXAMPLES_DIR = joinpath(pathof(Trixi) |> dirname |> dirname, "examples", "1d")
 
   @testset "elixir_euler_sedov_blast_wave.jl" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_sedov_blast_wave.jl"),
-      l2   = [1.2526428105949643, 0.06850036315669353, 0.9265758557535149],
-      linf = [2.987836852104084, 0.1706331519278507, 2.6658508877441838])
+      l2   = [1.250005061244617, 0.06878411345533507, 0.9264328311018613],
+      linf = [2.9766770877037168, 0.16838100902295852, 2.6655773445485798])
   end
 
   @testset "elixir_euler_sedov_blast_wave.jl with pressure" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_sedov_blast_wave.jl"),
-      l2   = [1.2983852642398792, 0.07961334122389492, 0.9270679298118678],
-      linf = [3.185530212032373, 0.2136435252219927, 2.6651572539845736],
-      shock_indicator_variable = pressure)
+      l2   = [1.297525985166995, 0.07964929522694145, 0.9269991156246368],
+      linf = [3.1773015255764427, 0.21331831536493773, 2.6650170188241047],
+      shock_indicator_variable = pressure,
+      cfl = 0.2)
   end
 
   @testset "elixir_euler_sedov_blast_wave.jl with density" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_sedov_blast_wave.jl"),
-      l2   = [1.2796976935143354, 0.07078122470157631, 0.9274308941700738],
-      linf = [3.1132929378257703, 0.17699767997572083, 2.66685149106963],
+      l2   = [1.2798798835860528, 0.07103461242058921, 0.9273792517187003],
+      linf = [3.1087017048015824, 0.17734706962928956, 2.666689753470263],
       shock_indicator_variable = density,
-      cfl = 0.5)
+      cfl = 0.2)
   end
 
   @testset "elixir_euler_blast_wave.jl" begin
diff --git a/test/test_examples_2d_parallel.jl b/test/test_examples_2d_parallel.jl
index 95d6df01a8..cbac8bcc33 100644
--- a/test/test_examples_2d_parallel.jl
+++ b/test/test_examples_2d_parallel.jl
@@ -60,7 +60,8 @@ const EXAMPLES_DIR = joinpath(pathof(Trixi) |> dirname |> dirname, "examples", "
   @testset "elixir_euler_source_terms.jl" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_source_terms.jl"),
       l2   = [8.517783186497567e-7, 1.2350199409361865e-6, 1.2350199409828616e-6, 4.277884398786315e-6],
-      linf = [8.357934254688004e-6, 1.0326389653148027e-5, 1.0326389654924384e-5, 4.4961900057316484e-5])
+      linf = [8.357934254688004e-6, 1.0326389653148027e-5, 1.0326389654924384e-5, 4.4961900057316484e-5],
+      rtol = 2000*sqrt(eps()))
   end
 
   @testset "elixir_euler_density_wave.jl" begin
@@ -73,7 +74,8 @@ const EXAMPLES_DIR = joinpath(pathof(Trixi) |> dirname |> dirname, "examples", "
   @testset "elixir_euler_nonperiodic.jl" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_nonperiodic.jl"),
       l2   = [2.3652137675654753e-6, 2.1386731303685556e-6, 2.138673130413185e-6, 6.009920290578574e-6],
-      linf = [1.4080448659026246e-5, 1.7581818010814487e-5, 1.758181801525538e-5, 5.9568540361709665e-5])
+      linf = [1.4080448659026246e-5, 1.7581818010814487e-5, 1.758181801525538e-5, 5.9568540361709665e-5],
+      rtol = 0.001)
   end
 
   @testset "elixir_euler_ec.jl" begin
@@ -85,13 +87,15 @@ const EXAMPLES_DIR = joinpath(pathof(Trixi) |> dirname |> dirname, "examples", "
   @testset "elixir_euler_vortex.jl" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_vortex.jl"),
       l2   = [3.6342636871275523e-6, 0.0032111366825032443, 0.0032111479254594345, 0.004545714785045611],
-      linf = [7.903587114788113e-5, 0.030561314311228993, 0.030502600162385596, 0.042876297246817074])
+      linf = [7.903587114788113e-5, 0.030561314311228993, 0.030502600162385596, 0.042876297246817074],
+      rtol = 0.001)
   end
 
   @testset "elixir_euler_vortex_shockcapturing.jl" begin
     @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_euler_vortex_shockcapturing.jl"),
       l2   = [3.80342739421474e-6, 5.561118953968859e-5, 5.564042529709319e-5, 0.0001570628548096201],
-      linf = [8.491382365727329e-5, 0.0009602965158113097, 0.0009669978616948516, 0.0030750353269972663])
+      linf = [8.491382365727329e-5, 0.0009602965158113097, 0.0009669978616948516, 0.0030750353269972663],
+      rtol = 0.001)
   end
 end
 
diff --git a/test/test_trixi.jl b/test/test_trixi.jl
index cec5478193..a996cb1625 100644
--- a/test/test_trixi.jl
+++ b/test/test_trixi.jl
@@ -20,7 +20,7 @@ macro test_trixi_include(elixir, args...)
   local l2   = get_kwarg(args, :l2, nothing)
   local linf = get_kwarg(args, :linf, nothing)
   local atol = get_kwarg(args, :atol, 200*eps())
-  local rtol = get_kwarg(args, :rtol, 0.001)
+  local rtol = get_kwarg(args, :rtol, sqrt(eps()))
   local kwargs = Pair{Symbol, Any}[]
   for arg in args
     if arg.head == :(=) && !(arg.args[1] in (:l2, :linf, :atol, :rtol))