diff --git a/src/tgbatest/Makefile.am b/src/tgbatest/Makefile.am
index c06f157ab..7866d0060 100644
--- a/src/tgbatest/Makefile.am
+++ b/src/tgbatest/Makefile.am
@@ -127,6 +127,7 @@ TESTS = \
   ltlcounter.test \
   basimul.test \
   satmin.test \
+  satmin2.test \
   spotlbtt.test \
   ltlcross.test \
   spotlbtt2.test \
diff --git a/src/tgbatest/satmin2.test b/src/tgbatest/satmin2.test
new file mode 100755
index 000000000..4bbe3db58
--- /dev/null
+++ b/src/tgbatest/satmin2.test
@@ -0,0 +1,50 @@
+
+#!/bin/sh
+# -*- coding: utf-8 -*-
+# Copyright (C) 2013 Laboratoire de Recherche et Développement
+# de l'Epita (LRDE).
+#
+# This file is part of Spot, a model checking library.
+#
+# Spot is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3 of the License, or
+# (at your option) any later version.
+#
+# Spot is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+# or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
+# License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+. ./defs
+set -e
+
+# Skip if $SATSOLVE is not installed.
+(${SATSOLVER-glucose} --help >/dev/null 2>&1) || exit 77
+
+
+# This is a counterexample for one of the optimization idea we had for
+# the SAT-based minimization.
+cat >input.tgba  <<EOF
+acc = "x";
+"1", "2", "a", "x";
+"1", "3", "!a",;
+"2", "1", "!a", "x";
+"2", "3", "a",;
+"3", "3", "a", "x";
+"3", "3", "!a",;
+EOF
+
+cat >expected <<EOF
+sub trans.: 2
+transitions: 2
+states: 1
+nondeterministic states: 0
+EOF
+
+../ltl2tgba -RS1 -kt -X input.tgba > output
+diff output expected
+