diff --git a/NEWS b/NEWS
index 47bc514b9..198f803c2 100644
--- a/NEWS
+++ b/NEWS
@@ -2,6 +2,15 @@ New in spot 2.0.2a (Not yet released)
 
   Nothing yet.
 
+  Bug fixes:
+
+  * The degen-lcache=1 option of the degeneralization algorithm (which
+    is a default option) did not behave exactly as documented: instead
+    of reusing the first level ever created for a state where the
+    choice of the level is free, it used the last level used.  This
+    caused some posterior simulation-based reductions to be less
+    efficient at reducing automata (on the average).
+
 New in spot 2.0.2 (2016-06-17)
 
   Documentation:
diff --git a/spot/twaalgos/degen.cc b/spot/twaalgos/degen.cc
index b73f2afc1..73663ed32 100644
--- a/spot/twaalgos/degen.cc
+++ b/spot/twaalgos/degen.cc
@@ -519,6 +519,8 @@ namespace spot
                             lvl = std::max(lvl_cache[d.first].first, lvl);
                           else if (use_lvl_cache == 2)
                             lvl = std::min(lvl_cache[d.first].first, lvl);
+                          else
+                            lvl = lvl_cache[d.first].first; // Do not change
                         }
                       lvl_cache[d.first] = std::make_pair(lvl, true);
                     }
diff --git a/tests/core/degendet.test b/tests/core/degendet.test
index 89c1dfa32..c335ced42 100755
--- a/tests/core/degendet.test
+++ b/tests/core/degendet.test
@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2011, 2015 Laboratoire de Recherche et Développement
+# Copyright (C) 2011, 2015, 2016 Laboratoire de Recherche et Développement
 # de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -23,7 +23,7 @@
 
 set -e
 
-# The following command, reported by Tomáš Babiak, used to output many
+# The following command, reported by Tomáš Babiak, used to output many
 # different automata, because state addresses were used to order the
 # successors in the degeneralization.
 
@@ -36,3 +36,10 @@ for i in 2 3 4 5; do
   ../ikwiad -r7 -x -R3 -N "XF(Gp2 | F(p0 U (p1 & (! p4 | p3))))" > out
   cmp out out1 || exit 1
 done
+
+# The next formula used to be translated into a 6-state automaton
+# instead of a 4-state automaton, because of an error in the
+# implementation of the degen-lcache=1 option causing the last level
+# used to be reused, instead of the first one.
+run 0 ltl2tgba -B -f '(b & Fa) U XXG(a M Gb)' --stats=%s,%t >out
+test "4,14" = "`cat out`"
diff --git a/tests/core/ltl2ta.test b/tests/core/ltl2ta.test
index e95e92513..ec5298a8c 100755
--- a/tests/core/ltl2ta.test
+++ b/tests/core/ltl2ta.test
@@ -1,7 +1,7 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015 Laboratoire de
-# Recherche et Développement de l'Epita (LRDE).
+# Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015, 2016 Laboratoire
+# de Recherche et Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@@ -170,12 +170,12 @@ in: Fa & b & GFc & Gd
 -TA -DS -RT          |     12 |    126 |      5
 -TA -DS -lv          |     29 |    315 |     13
 -TA -DS -lv -RT      |     13 |    140 |      4
--TA -DS -sp          |     28 |    309 |     12
--TA -DS -sp -RT      |     12 |    137 |      3
+-TA -DS -sp          |     28 |    306 |     12
+-TA -DS -sp -RT      |     12 |    134 |      3
 -TA -DS -lv -sp      |     29 |    315 |     13
 -TA -DS -lv -sp -RT  |     13 |    140 |      4
--x -TA -DS -in       |     29 |    254 |      9
--x -TA -DS -in -RT   |     12 |     96 |      3
+-x -TA -DS -in       |     29 |    240 |      9
+-x -TA -DS -in -RT   |     12 |     93 |      3
 in: Fa & a & GFc & Gc
 -TGTA                |      4 |      8 |    XXX
 -TGTA -RT            |      3 |      6 |    XXX
@@ -401,15 +401,15 @@ in: FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)
 -TA -lv -sp          |     45 |    676 |      9
 -TA -lv -sp -RT      |     35 |    566 |      4
 -TA -DS              |     54 |    722 |     26
--TA -DS -RT          |     42 |    600 |     19
+-TA -DS -RT          |     42 |    608 |     18
 -TA -DS -lv          |     55 |    800 |     19
--TA -DS -lv -RT      |     44 |    694 |     13
--TA -DS -sp          |     54 |    795 |     18
--TA -DS -sp -RT      |     43 |    683 |     12
+-TA -DS -lv -RT      |     44 |    702 |     13
+-TA -DS -sp          |     54 |    789 |     18
+-TA -DS -sp -RT      |     43 |    686 |     12
 -TA -DS -lv -sp      |     55 |    800 |     19
--TA -DS -lv -sp -RT  |     44 |    694 |     13
--x -TA -DS -in       |     55 |    700 |     11
--x -TA -DS -in -RT   |     39 |    566 |      8
+-TA -DS -lv -sp -RT  |     44 |    702 |     13
+-x -TA -DS -in       |     55 |    694 |     11
+-x -TA -DS -in -RT   |     41 |    597 |      8
 in: G(F(GWaitLeft7 U Idle4) U (WaitLeft2 M IsEating2))
 -TGTA                |     69 |   1539 |    XXX
 -TGTA -RT            |     49 |    935 |    XXX
@@ -422,15 +422,15 @@ in: G(F(GWaitLeft7 U Idle4) U (WaitLeft2 M IsEating2))
 -TA -lv -sp          |     68 |   1443 |     16
 -TA -lv -sp -RT      |     56 |   1179 |     15
 -TA -DS              |    124 |   2964 |     44
--TA -DS -RT          |    100 |   2285 |     42
+-TA -DS -RT          |     96 |   2099 |     42
 -TA -DS -lv          |    125 |   3028 |     42
--TA -DS -lv -RT      |    101 |   2339 |     40
+-TA -DS -lv -RT      |     97 |   2149 |     40
 -TA -DS -sp          |    124 |   3012 |     41
--TA -DS -sp -RT      |    100 |   2324 |     39
+-TA -DS -sp -RT      |     96 |   2134 |     39
 -TA -DS -lv -sp      |    125 |   3028 |     42
--TA -DS -lv -sp -RT  |    101 |   2339 |     40
+-TA -DS -lv -sp -RT  |     97 |   2149 |     40
 -x -TA -DS -in       |    125 |   1838 |     25
--x -TA -DS -in -RT   |     89 |   1344 |     25
+-x -TA -DS -in -RT   |     87 |   1296 |     25
 EOF
 
 sed -n 's/in: \(.*\)/\1/p' checkta.txt > input.txt