diff --git a/dune/tectonic/time-stepping/adaptivetimestepper.cc b/dune/tectonic/time-stepping/adaptivetimestepper.cc
index d9ef1c5aa09e303d457be8d9f3ee6a0fb1d479d7..d8b009083d9fece76764f658da1ba3aad9a387bc 100644
--- a/dune/tectonic/time-stepping/adaptivetimestepper.cc
+++ b/dune/tectonic/time-stepping/adaptivetimestepper.cc
@@ -43,9 +43,11 @@ AdaptiveTimeStepper<Factory, ContactNetwork, Updaters, ErrorNorms>::AdaptiveTime
         Updaters &current,
         double relativeTime,
         double relativeTau,
+        double minTau,
         std::function<bool(Updaters &, Updaters &)> mustRefine)
     : relativeTime_(relativeTime),
       relativeTau_(relativeTau),
+      minTau_(minTau),
       stepBase_(stepBase),
       contactNetwork_(contactNetwork),
       current_(current),
@@ -133,6 +135,11 @@ int AdaptiveTimeStepper<Factory, ContactNetwork, Updaters, ErrorNorms>::refine(U
     const auto& currentNBodyAssembler = contactNetwork_.nBodyAssembler();
 
     while (true) {
+        if (relativeTau_ / 2.0 <= minTau_) {
+          std::cout << "Sufficiently refined!" << std::endl;
+          break;
+        }
+
         setDeformation(current_);
         //auto F1_linearSolver = makeLinearSolver();
         auto F1_Step = Step(stepBase_, current_, currentNBodyAssembler, relativeTime_, relativeTau_ / 2.0, iterationRegister_);
@@ -236,7 +243,7 @@ int AdaptiveTimeStepper<Factory, ContactNetwork, Updaters, ErrorNorms>::determin
 
         F1 = F1_Step.get();
 
-        if (strategy>-1) {
+        if (strategy>-1 && relativeTau_ / 2.0 > minTau_) {
             setDeformation(F1.updaters);
             //auto F2_linearSolver = makeLinearSolver();
             auto&& nBodyAssembler = step(currentNBodyAssembler);
diff --git a/dune/tectonic/time-stepping/adaptivetimestepper.hh b/dune/tectonic/time-stepping/adaptivetimestepper.hh
index 2d11dd9db763578ee9555e5427464d7363991969..43b16ec602e954ab1ecd99f6f8e43b16d7b220a8 100644
--- a/dune/tectonic/time-stepping/adaptivetimestepper.hh
+++ b/dune/tectonic/time-stepping/adaptivetimestepper.hh
@@ -51,6 +51,7 @@ class AdaptiveTimeStepper {
                       Updaters &current,
                       double relativeTime,
                       double relativeTau,
+                      double minTau,
                       std::function<bool(Updaters &, Updaters &)> mustRefine);
 
   bool reachedEnd();
@@ -59,6 +60,7 @@ class AdaptiveTimeStepper {
 
   double relativeTime_;
   double relativeTau_;
+  const double minTau_;
 
 private:
   void setDeformation(const Updaters& updaters);