diff --git a/prism/src/simulator/sampler/SamplerBoundedUntilCont.java b/prism/src/simulator/sampler/SamplerBoundedUntilCont.java
index ae97665d..0cd41b07 100644
--- a/prism/src/simulator/sampler/SamplerBoundedUntilCont.java
+++ b/prism/src/simulator/sampler/SamplerBoundedUntilCont.java
@@ -167,7 +167,7 @@ public class SamplerBoundedUntilCont extends SamplerBoolean
 	@Override
 	public boolean needsBoundedNumSteps()
 	{
-		// Always bounded (although we don't know the exact num steps, just the time bound)
-		return true;
+		// Bounded if there is a non-finite upper-bound (although we don't know the exact num steps, just the time bound)
+		return ub < Double.POSITIVE_INFINITY;
 	}
 }
diff --git a/prism/src/simulator/sampler/SamplerBoundedUntilDisc.java b/prism/src/simulator/sampler/SamplerBoundedUntilDisc.java
index ff922410..b6f421ef 100644
--- a/prism/src/simulator/sampler/SamplerBoundedUntilDisc.java
+++ b/prism/src/simulator/sampler/SamplerBoundedUntilDisc.java
@@ -137,7 +137,7 @@ public class SamplerBoundedUntilDisc extends SamplerBoolean
 	@Override
 	public boolean needsBoundedNumSteps()
 	{
-		// Always bounded
-		return true;
+		// Bounded if there is an upper bound
+		return haveUpperBound;
 	}
 }