diff --git a/ChangeLog b/ChangeLog
index 7c470245f..bad990033 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,13 @@
+2006-04-05  Alexandre Duret-Lutz  <adl@src.lip6.fr>
+
+	* src/tgbaalgos/gtec/gtec.cc, src/tgbaalgos/gtec/gtec.hh:
+	(couvreur99_check_shy_ssp): Add a onepass_ attribute to
+	disable the "shyness", and do not increment pos before calling
+	find_state since gspn's implementation uses it.
+	* iface/gspn/ssp.cc: Enable "onepass_" for all "shy" variants,
+	and also fix find_state for the case where onepass_ is
+	disabled (but I do not yet know why the latter fix isn't enough).
+
 2006-02-15  Alexandre Duret-Lutz  <adl@src.lip6.fr>
 
 	* src/tgbaalgos/gtec/gtec.cc: Add a third level hash, to split
diff --git a/iface/gspn/ssp.cc b/iface/gspn/ssp.cc
index 213635c9d..5c3d2d288 100644
--- a/iface/gspn/ssp.cc
+++ b/iface/gspn/ssp.cc
@@ -994,6 +994,8 @@ namespace spot
 	inclusion_count_stack(0),
 	stack_inclusion(stack_inclusion)
     {
+      onepass_ = true;
+
       stats["inclusion count heap"] =
 	static_cast<spot::unsigned_statistics::unsigned_fun>
 	(&couvreur99_check_shy_ssp::get_inclusion_count_heap);
@@ -1046,6 +1048,7 @@ namespace spot
       const state_gspn_ssp* s_ = dynamic_cast<const state_gspn_ssp*>(s);
       const void* cont = container_(s_->left());
       contained_map::const_iterator i = contained.find(cont);
+
       if (i != contained.end())
 	{
 	  f_map::const_iterator k = i->second.find(s_->right());
@@ -1094,13 +1097,19 @@ namespace spot
 			      Diff_succ(old_state->left(), new_state->left(),
 					&succ_tgba_, &size_tgba_);
 
+			      succ_queue::iterator old;
+			      if (pos == queue.end())
+				old = queue.begin();
+			      else
+				old = pos;
+
 			      for (size_t i = 0; i < size_tgba_; i++)
 				{
 				  state_gspn_ssp* s =
 				    new state_gspn_ssp
 				    (succ_tgba_[i],
 				     old_state->right()->clone());
-				  queue.push_back(successor(queue.begin()->acc,
+				  queue.push_back(successor(old->acc,
 							    s));
 				  inc_depth();
 				}
@@ -1166,6 +1175,8 @@ namespace spot
 			     numbered_state_heap_ssp_factory_semi::instance()),
 	inclusion_count(0)
     {
+      onepass_ = true;
+
       stats["find_state count"] =
 	static_cast<spot::unsigned_statistics::unsigned_fun>
 	(&couvreur99_check_shy_semi_ssp::get_inclusion_count);
diff --git a/src/tgbaalgos/gtec/gtec.cc b/src/tgbaalgos/gtec/gtec.cc
index d4897c4a4..adb1cb030 100644
--- a/src/tgbaalgos/gtec/gtec.cc
+++ b/src/tgbaalgos/gtec/gtec.cc
@@ -322,6 +322,7 @@ namespace spot
     group_ = o.get("group", 1);
     group2_ = o.get("group2", 0);
     group_ |= group2_;
+    onepass_ = o.get("onepass", 0);
 
     // Setup depth-first search from the initial state.
     const state* i = ecs_->aut->get_init_state();
@@ -364,7 +365,7 @@ namespace spot
   couvreur99_check_shy::check()
   {
     // Position in the loop seeking known successors.
-    succ_queue::iterator pos = todo.back().q.begin();
+    pos = todo.back().q.begin();
 
     for (;;)
       {
@@ -429,13 +430,18 @@ namespace spot
 	// which state we are considering.  Otherwise just pick the
 	// first one.
 	succ_queue::iterator old;
+	if (onepass_)
+	  pos = queue.end();
 	if (pos == queue.end())
 	  old = queue.begin();
 	else
-	  old = pos++;
+	  old = pos;
 	successor succ = *old;
-
+	// Beware: the implementation of find_state in ifage/gspn/ssp.cc
+	// uses POS and modify QUEUE.
 	numbered_state_heap::state_index_p sip = find_state(succ.s);
+	if (pos != queue.end())
+	  ++pos;
 	int* i = sip.second;
 
 	if (!i)
diff --git a/src/tgbaalgos/gtec/gtec.hh b/src/tgbaalgos/gtec/gtec.hh
index 7c31e4fb5..85110aff5 100644
--- a/src/tgbaalgos/gtec/gtec.hh
+++ b/src/tgbaalgos/gtec/gtec.hh
@@ -221,6 +221,9 @@ namespace spot
     //   (ACCEPTANCE_CONDITIONS, STATE) pairs.
     typedef std::list<successor> succ_queue;
 
+    // Position in the loop seeking known successors.
+    succ_queue::iterator pos;
+
     struct todo_item
     {
       const state* s;
@@ -239,6 +242,10 @@ namespace spot
     // If the "group2" option is set (it implies "group"), we
     // reprocess the successor states of SCC that have been merged.
     bool group2_;
+    // If the onepass option is true, do only one pass.  This cancels
+    // all the "shyness" of the algorithm, but we need the framework
+    // of the implementation when working with GreatSPN.
+    bool onepass_;
 
     /// \brief find the SCC number of a unprocessed state.
     ///