diff --git a/NEWS b/NEWS
index 17619300b..cf7f5440e 100644
--- a/NEWS
+++ b/NEWS
@@ -14,6 +14,9 @@ New in spot 1.1.4a (not relased)
     temporary files are created and if they should be erased.  Read
     the man page of ltlcross for detail.
 
+  * Degeneralization was not indempotant on automata with an accepting
+    initial state that was on a cycle, but without self-loop.
+
   * Cleanup of exported symbols
 
     All symbols in the library now have hidden visibility on ELF systems.
diff --git a/src/tgbaalgos/degen.cc b/src/tgbaalgos/degen.cc
index 26eff12b9..b9ca87752 100644
--- a/src/tgbaalgos/degen.cc
+++ b/src/tgbaalgos/degen.cc
@@ -188,8 +188,7 @@ namespace spot
 
         acc = temp;
         unsigned next = slevel;
-        while (next < order_.size()
-               && (acc & order_[next]) == order_[next])
+        while (next < order_.size() && bdd_implies(order_[next], acc))
           ++next;
         return next;
       }
@@ -314,8 +313,8 @@ namespace spot
     const state* s0 = uniq(a->get_init_state());
     degen_state s(s0, 0);
 
-    // As an heuristic, if the initial state has accepting self-loops,
-    // start the degeneralization on the accepting level.
+    // As an heuristic, if the initial state at least one accepting
+    // self-loop, start the degeneralization on the accepting level.
     {
       bdd all = a->all_acceptance_conditions();
       tgba_succ_iterator* it = a->succ_iter(s0);
@@ -335,6 +334,18 @@ namespace spot
         }
       delete it;
     }
+    // Otherwise, check for acceptance conditions common to all
+    // outgoing transitions, and assume we have already seen these and
+    // start on the associated level.
+    if (s.second == 0)
+      {
+	bdd acc = outgoing.common_acc(s.first);
+	if (use_cust_acc_orders)
+	  s.second = orders.next_level(m.initial(), s.second, acc);
+	else
+	  while (s.second < order.size() && bdd_implies(order[s.second], acc))
+	    ++s.second;
+      }
 
 #ifdef DEGEN_DEBUG
     std::map<const state*, int>names;
@@ -426,7 +437,7 @@ namespace spot
                 //    1=>1, 1=>2, 2->2, 2->1 This is already an SBA,
                 //    with 1 as accepting state.  However if you try
                 //    degeralize it without ignoring *prev, you'll get
-                //    two copies of states 2, depending on whether we
+                //    two copies of state 2, depending on whether we
                 //    reach it using 1=>2 or from 2->2.  If this
                 //    example was not clear, uncomment the following
                 //    "if" block, and play with the "degenid.test"
@@ -485,7 +496,7 @@ namespace spot
                   }
                 else
                   {
-                  // If using custom acc orders, get next level for this scc
+		    // If using custom acc orders, get next level for this scc
                     if (use_cust_acc_orders)
                       d.second = orders.next_level(scc, next, acc);
                     // Else compute level according the global acc order
@@ -495,7 +506,7 @@ namespace spot
                         // acceptance sets common to the outgoing transitions of
                         // the destination state.
                         while (next < order.size()
-                               && (acc & order[next]) == order[next])
+			       && bdd_implies(order[next], acc))
                           ++next;
 
                         d.second = next;
diff --git a/src/tgbatest/degenid.test b/src/tgbatest/degenid.test
index fdd0abc72..ff5e9bb50 100755
--- a/src/tgbatest/degenid.test
+++ b/src/tgbatest/degenid.test
@@ -1,5 +1,5 @@
 #!/bin/sh
-# Copyright (C) 2011 Laboratoire de Recherche et Développement
+# Copyright (C) 2011, 2013 Laboratoire de Recherche et Développement
 # de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -36,3 +36,32 @@ for f in 'FGa|GFb' 'GFa & GFb & GFc' 'GF(a->FGb)&GF(c->FGd)'; do
     done
   done
 done
+
+
+# This is another 6-state degeneralized automaton that
+# we used the "redegeneralize" to a 8-state BA...
+cat > bug <<EOF
+acc = "1";
+"1", "2", "!b | !a", "1";
+"1", "5", "a & b", "1";
+"2", "2", "b & !a", "1";
+"2", "3", "!b & !a", "1";
+"2", "4", "a", "1";
+"5", "1", "a & !b",;
+"5", "2", "!b & !a",;
+"5", "5", "a & b",;
+"5", "6", "b & !a",;
+"3", "1", "a & b",;
+"3", "2", "b & !a",;
+"3", "3", "!b & !a",;
+"3", "4", "a & !b",;
+"4", "1", "b",;
+"4", "5", "a & !b",;
+"4", "6", "!b & !a",;
+"6", "1", "!b",;
+"6", "3", "b & !a",;
+"6", "4", "a & b",;
+EOF
+
+run 0 ../ltl2tgba -ks -X -DS bug > out
+grep 'states: 6' out