diff --git a/framework/include/timesteppers/ConstantDT.h b/framework/include/timesteppers/ConstantDT.h
index 2f9c08f8be72..0f0a41e4e0ea 100644
--- a/framework/include/timesteppers/ConstantDT.h
+++ b/framework/include/timesteppers/ConstantDT.h
@@ -30,7 +30,10 @@ class ConstantDT : public TimeStepper
 protected:
   virtual Real computeInitialDT();
   virtual Real computeDT();
-};
 
+private:
+  const Real _constant_dt;
+  const Real _growth_factor;
+};
 
 #endif /* CONSTANTDT_H */
diff --git a/framework/src/timesteppers/ConstantDT.C b/framework/src/timesteppers/ConstantDT.C
index a5f85c2f3786..c456df289aea 100644
--- a/framework/src/timesteppers/ConstantDT.C
+++ b/framework/src/timesteppers/ConstantDT.C
@@ -16,26 +16,38 @@
 #include "FEProblem.h"
 #include "Transient.h"
 
+namespace
+{
+const std::string dt_name = "dt";
+const std::string growth_factor_name = "growth_factor";
+}
+
 template<>
 InputParameters validParams<ConstantDT>()
 {
   InputParameters params = validParams<TimeStepper>();
-  params.addRequiredParam<Real>("dt", "Size of the time step");
+  params.addRequiredParam<Real>( dt_name, "Size of the time step" );
+  params.addRangeCheckedParam<Real>( growth_factor_name, 2, growth_factor_name + ">=1",
+    "Maximum ratio of new to previous timestep sizes following a step that required the time"
+    " step to be cut due to a failed solve." );
   return params;
 }
 
 ConstantDT::ConstantDT(const std::string & name, InputParameters parameters) :
-    TimeStepper(name, parameters)
-{}
+    TimeStepper( name, parameters ),
+    _constant_dt( getParam<Real>( dt_name ) ),
+    _growth_factor( getParam<Real>( growth_factor_name ) )
+{
+}
 
 Real
 ConstantDT::computeInitialDT()
 {
-  return getParam<Real>("dt");
+  return _constant_dt;
 }
 
 Real
 ConstantDT::computeDT()
 {
-  return getCurrentDT();
+  return std::min( _constant_dt, _growth_factor * getCurrentDT() );
 }
diff --git a/test/tests/time_steppers/failure/gold/constant_failure_out.e b/test/tests/time_steppers/failure/gold/constant_failure_out.e
index 8dd2571cda6d..e997d9536adc 100644
Binary files a/test/tests/time_steppers/failure/gold/constant_failure_out.e and b/test/tests/time_steppers/failure/gold/constant_failure_out.e differ