diff --git a/src/ltltest/remove_x.test b/src/ltltest/remove_x.test
index a8f3f4931..e81dca283 100755
--- a/src/ltltest/remove_x.test
+++ b/src/ltltest/remove_x.test
@@ -1,5 +1,5 @@
 #! /bin/sh
-# Copyright (C) 2013 Laboratoire de Recherche et Developement to
+# Copyright (C) 2013, 2014 Laboratoire de Recherche et Developement to
 # l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -27,3 +27,13 @@ run 0 ../../bin/ltlfilt --stutter-invariant -f 'F(!a & Xa & Xb)'
 
 run 1 ../../bin/ltlfilt --stutter-invariant -f 'F(Xa & Xb)'
 
+run 0 ../../bin/ltlfilt --remove-x -f 'F(!a & Xa & Xb)' > out
+grep -v X out
+run 0 ../../bin/ltlfilt --stutter-invariant -F 'out'
+
+
+run 1 ../../bin/ltlfilt --stutter-invariant -f 'F(!a & Xb)'
+run 0 ../../bin/ltlfilt --remove-x -f 'F(!a & Xb)' > out
+grep -v X out
+# The output is stutter invariant, even if the input wasn't.
+run 0 ../../bin/ltlfilt --stutter-invariant -F 'out'