diff --git a/lib/OrdinaryDiffEqBDF/src/controllers.jl b/lib/OrdinaryDiffEqBDF/src/controllers.jl
index cba5dcb56b..8ca920f813 100644
--- a/lib/OrdinaryDiffEqBDF/src/controllers.jl
+++ b/lib/OrdinaryDiffEqBDF/src/controllers.jl
@@ -45,7 +45,7 @@ function step_accept_controller!(integrator, alg::QNDF{max_order}, q) where {max
             Fₖ₋₁ = inv(zₖ₋₁)
             if zₖ₋₁ <= 0.1
                 hₖ₋₁ = 10 * h
-            elseif 1 / 10 < zₖ₋₁ <= 1.3
+            elseif zₖ₋₁ <= 1.3
                 hₖ₋₁ = Fₖ₋₁ * h
             end
             if hₖ₋₁ > hₖ
@@ -89,14 +89,6 @@ function step_accept_controller!(integrator, alg::QNDF{max_order}, q) where {max
     return integrator.dt / q
 end
 
-function step_reject_controller!(integrator, ::QNDF)
-    bdf_step_reject_controller!(integrator, integrator.cache.EEst1)
-end
-
-function step_reject_controller!(integrator, ::FBDF)
-    bdf_step_reject_controller!(integrator, integrator.cache.terkm1)
-end
-
 function bdf_step_reject_controller!(integrator, EEst1)
     k = integrator.cache.order
     h = integrator.dt
@@ -122,7 +114,7 @@ function bdf_step_reject_controller!(integrator, EEst1)
         Fₖ₋₁ = inv(zₖ₋₁)
         if zₖ₋₁ <= 10
             hₖ₋₁ = Fₖ₋₁ * h
-        elseif zₖ₋₁ > 10
+        else # zₖ₋₁ > 10
             hₖ₋₁ = 0.1 * h
         end
         if integrator.cache.consfailcnt > 2 || hₖ₋₁ > hₖ
@@ -138,6 +130,14 @@ function bdf_step_reject_controller!(integrator, EEst1)
     integrator.cache.order = kₙ
 end
 
+function step_reject_controller!(integrator, ::QNDF)
+    bdf_step_reject_controller!(integrator, integrator.cache.EEst1)
+end
+
+function step_reject_controller!(integrator, ::FBDF)
+    bdf_step_reject_controller!(integrator, integrator.cache.terkm1)
+end
+
 function post_newton_controller!(integrator, alg::FBDF)
     (; cache) = integrator
     if cache.order > 1 && cache.nlsolver.nfails >= 3
diff --git a/lib/OrdinaryDiffEqBDF/test/dae_ad_tests.jl b/lib/OrdinaryDiffEqBDF/test/dae_ad_tests.jl
index cdb037f45e..686d85bc88 100644
--- a/lib/OrdinaryDiffEqBDF/test/dae_ad_tests.jl
+++ b/lib/OrdinaryDiffEqBDF/test/dae_ad_tests.jl
@@ -36,12 +36,14 @@ f_mm = ODEFunction{true}(f_ode, mass_matrix = M)
 prob_mm = ODEProblem(f_mm, u₀, tspan, p)
 f_mm_oop = ODEFunction{false}(f_ode, mass_matrix = M)
 prob_mm_oop = ODEProblem(f_mm_oop, u₀, tspan, p)
-@test_broken sol1 = @inferred solve(
+if VERSION >= v"1.12"
+sol1 = @inferred solve(
     prob, DFBDF(autodiff = afd_cs3), dt = 1e-5, abstol = 1e-8, reltol = 1e-8)
-@test_broken sol2 = @inferred solve(
+sol2 = @inferred solve(
     prob_oop, DFBDF(autodiff = afd_cs3), dt = 1e-5, abstol = 1e-8, reltol = 1e-8)
-@test_broken sol3 = @inferred solve(
+sol3 = @inferred solve(
     prob_mm, FBDF(autodiff = afd_cs3), dt = 1e-5, abstol = 1e-8, reltol = 1e-8)
+end
 
 # These tests flex differentiation of the solver and through the initialization
 # To only test the solver part and isolate potential issues, set the initialization to consistent