diff --git a/ChangeLog b/ChangeLog
index d043e9d13..01a4c04c0 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,14 @@
+2005-01-28  Alexandre Duret-Lutz  <adl@src.lip6.fr>
+
+	* src/tgbaalgos/emptiness_stats.hh: Make sure depth() >= 0.
+	* src/tgbaalgos/gtec/gtec.hh (couvreur99_check, couvreur99_check_shy):
+	Add the poprem option.
+	* src/tgbaalgos/gtec/gtec.cc: Implement it.
+	* src/tgbaalgos/gtec/sccstack.cc, src/tgbaalgos/gtec/sccstack.hh
+	(scc_stack::rem, scc_stack::clear_rem,
+	scc_stack::connected_component::rem): New.
+	* src/tgbatest/ltl2tgba.cc, src/tgbatest/randtgba.cc: Add rem variants.
+
 2005-01-28  Denis Poitrenaud  <Denis.Poitrenaud@lip6.fr>
 
 	* src/tgbatest/dfs.test, src/tgbatest/emptchk.test,
diff --git a/src/tgbaalgos/emptiness_stats.hh b/src/tgbaalgos/emptiness_stats.hh
index 23b85e1e3..185f8c860 100644
--- a/src/tgbaalgos/emptiness_stats.hh
+++ b/src/tgbaalgos/emptiness_stats.hh
@@ -22,6 +22,8 @@
 #ifndef SPOT_TGBAALGOS_EMPTINESS_STATS_HH
 # define SPOT_TGBAALGOS_EMPTINESS_STATS_HH
 
+#include <cassert>
+
 namespace spot
 {
 
@@ -42,7 +44,7 @@ namespace spot
     }
 
     void
-    set_states(int n)
+    set_states(unsigned n)
     {
       states_ = n;
     }
@@ -60,7 +62,7 @@ namespace spot
     }
 
     void
-    inc_depth(int n = 1)
+    inc_depth(unsigned n = 1)
     {
       depth_ += n;
       if (depth_ > max_depth_)
@@ -68,8 +70,9 @@ namespace spot
     }
 
     void
-    dec_depth(int n = 1)
+    dec_depth(unsigned n = 1)
     {
+      assert(depth_ >= n);
       depth_ -= n;
     }
 
diff --git a/src/tgbaalgos/gtec/ce.cc b/src/tgbaalgos/gtec/ce.cc
index 023c10465..c75e3c41d 100644
--- a/src/tgbaalgos/gtec/ce.cc
+++ b/src/tgbaalgos/gtec/ce.cc
@@ -86,7 +86,7 @@ namespace spot
   couvreur99_check_result::acss_states() const
   {
     int count = 0;
-    int scc_root = ecs_->root.s.top().index;
+    int scc_root = ecs_->root.top().index;
 
     numbered_state_heap_const_iterator* i = ecs_->h->iterator();
     for (i->first(); !i->done(); i->next())
@@ -184,7 +184,7 @@ namespace spot
 		  couvreur99_check_result* r, bdd& acc_to_traverse)
 	    : bfs_steps(ecs->aut), ecs(ecs), r(r),
 	      acc_to_traverse(acc_to_traverse),
-	      scc_root(ecs->root.s.top().index)
+	      scc_root(ecs->root.top().index)
 	  {
 	  }
 
@@ -222,6 +222,7 @@ namespace spot
 	} b(ecs_, this, acc_to_traverse);
 
 	substart = b.search(substart, run_->cycle);
+	assert(substart);
       }
     while (acc_to_traverse != bddfalse || substart != ecs_->cycle_seed);
   }
diff --git a/src/tgbaalgos/gtec/gtec.cc b/src/tgbaalgos/gtec/gtec.cc
index 9f40b426f..82d7a6e63 100644
--- a/src/tgbaalgos/gtec/gtec.cc
+++ b/src/tgbaalgos/gtec/gtec.cc
@@ -30,8 +30,9 @@ namespace spot
   }
 
   couvreur99_check::couvreur99_check(const tgba* a,
+				     bool poprem,
 				     const numbered_state_heap_factory* nshf)
-    : emptiness_check(a)
+    : emptiness_check(a), poprem_(poprem)
   {
     ecs_ = new couvreur99_check_status(a, nshf);
   }
@@ -44,6 +45,23 @@ namespace spot
   void
   couvreur99_check::remove_component(const state* from)
   {
+    // If rem has been updated, removing states is very easy.
+    if (poprem_)
+      {
+	assert(!ecs_->root.rem().empty());
+	dec_depth(ecs_->root.rem().size());
+	std::list<const state*>::iterator i;
+	for (i = ecs_->root.rem().begin(); i != ecs_->root.rem().end(); ++i)
+	  {
+	    numbered_state_heap::state_index_p spi = ecs_->h->index(*i);
+	    assert(spi.first == *i);
+	    assert(*spi.second != -1);
+	    *spi.second = -1;
+	  }
+	// ecs_->root.rem().clear();
+	return;
+      }
+
     // Remove from H all states which are reachable from state FROM.
 
     // Stack of iterators towards states to remove.
@@ -57,7 +75,6 @@ namespace spot
     assert(spi.first == from);
     assert(*spi.second != -1);
     *spi.second = -1;
-    dec_depth(); // FIXME: check once remove_component() is revamped.
     tgba_succ_iterator* i = ecs_->aut->succ_iter(from);
 
     for (;;)
@@ -65,7 +82,7 @@ namespace spot
 	// Remove each destination of this iterator.
 	for (i->first(); !i->done(); i->next())
 	  {
-	    // FIXME: inc_transitions();
+	    inc_transitions();
 
 	    state* s = i->current_state();
 	    numbered_state_heap::state_index_p spi = ecs_->h->index(s);
@@ -81,7 +98,6 @@ namespace spot
 	    if (*spi.second != -1)
 	      {
 		*spi.second = -1;
-		dec_depth(); // FIXME: check after revamping.
 		to_remove.push(ecs_->aut->succ_iter(spi.first));
 	      }
 	  }
@@ -139,20 +155,28 @@ namespace spot
 
 	    // Backtrack TODO.
 	    todo.pop();
-	    // FIXME: dec_depth();
+	    dec_depth();
 
+	    // If poprem is used, fill rem with any component removed,
+	    // so that remove_component() does not have to traverse
+	    // the SCC again.
+	    numbered_state_heap::state_index_p spi = ecs_->h->index(curr);
+	    assert(spi.first);
+	    if (poprem_)
+	      {
+		ecs_->root.rem().push_front(spi.first);
+		inc_depth();
+	      }
 	    // When backtracking the root of an SCC, we must also
 	    // remove that SCC from the ARC/ROOT stacks.  We must
 	    // discard from H all reachable states from this SCC.
-	    numbered_state_heap::state_index_p spi = ecs_->h->index(curr);
-	    assert(spi.first);
 	    assert(!ecs_->root.empty());
 	    if (ecs_->root.top().index == *spi.second)
 	      {
 		assert(!arc.empty());
 		arc.pop();
-		ecs_->root.pop();
 		remove_component(curr);
+		ecs_->root.pop();
 	      }
 
 	    delete succ;
@@ -203,12 +227,14 @@ namespace spot
 	// top of ROOT that have an index greater to the one of
 	// the SCC of S2 (called the "threshold").
 	int threshold = *spi.second;
+	std::list<const state*> rem;
 	while (threshold < ecs_->root.top().index)
 	  {
 	    assert(!ecs_->root.empty());
 	    assert(!arc.empty());
 	    acc |= ecs_->root.top().condition;
 	    acc |= arc.top();
+	    rem.splice(rem.end(), ecs_->root.rem());
 	    ecs_->root.pop();
 	    arc.pop();
 	  }
@@ -219,6 +245,7 @@ namespace spot
 
 	// Accumulate all acceptance conditions into the merged SCC.
 	ecs_->root.top().condition |= acc;
+	ecs_->root.rem().splice(ecs_->root.rem().end(), rem);
 
 	if (ecs_->root.top().condition
 	    == ecs_->aut->all_acceptance_conditions())
@@ -261,10 +288,11 @@ namespace spot
   //////////////////////////////////////////////////////////////////////
 
   couvreur99_check_shy::couvreur99_check_shy(const tgba* a,
+					     bool poprem,
 					     bool group,
 					     const numbered_state_heap_factory*
 					     nshf)
-    : couvreur99_check(a, nshf), num(1), group_(group)
+    : couvreur99_check(a, poprem, nshf), num(1), group_(group)
   {
     // Setup depth-first search from the initial state.
     todo.push_back(todo_item(0, 0));
@@ -297,8 +325,8 @@ namespace spot
 	dec_depth(todo.back().q.size() + 1);
 	todo.pop_back();
       }
-    // FIXME: enable after revamping remove_component().
-    // assert(depth() == 0);
+    dec_depth(ecs_->root.clear_rem());
+    assert(depth() == 0);
   }
 
   emptiness_check_result*
@@ -318,18 +346,30 @@ namespace spot
 	    // We have explored all successors of state CURR.
 	    const state* curr = todo.back().s;
 	    int index = todo.back().n;
+
 	    // Backtrack TODO.
 	    todo.pop_back();
-	    // FIXME: dec_depth();
+	    dec_depth();
+
 	    if (todo.empty())
 	      {
 		// This automaton recognizes no word.
 		set_states(ecs_->states());
-		// FIXME: enable after revamping remove_component().
-		// assert(depth() == 0);
+		assert(poprem_ || depth() == 0);
 		return 0;
 	      }
 
+	    // If poprem is used, fill rem with any component removed,
+	    // so that remove_component() does not have to traverse
+	    // the SCC again.
+	    if (poprem_)
+	      {
+		numbered_state_heap::state_index_p spi = ecs_->h->index(curr);
+		assert(spi.first);
+		ecs_->root.rem().push_front(spi.first);
+		inc_depth();
+	      }
+
 	    // When backtracking the root of an SCC, we must also
 	    // remove that SCC from the ARC/ROOT stacks.  We must
 	    // discard from H all reachable states from this SCC.
@@ -338,8 +378,8 @@ namespace spot
 	      {
 		assert(!arc.empty());
 		arc.pop();
-		ecs_->root.pop();
 		remove_component(curr);
+		ecs_->root.pop();
 	      }
 	    continue;
 	  }
@@ -418,12 +458,14 @@ namespace spot
 	    // an index greater to the one of the SCC of S2
 	    // (called the "threshold").
 	    int threshold = *i;
+	    std::list<const state*> rem;
 	    while (threshold < ecs_->root.top().index)
 	      {
 		assert(!ecs_->root.empty());
 		assert(!arc.empty());
 		acc |= ecs_->root.top().condition;
 		acc |= arc.top();
+		rem.splice(rem.end(), ecs_->root.rem());
 		ecs_->root.pop();
 		arc.pop();
 	      }
@@ -435,6 +477,7 @@ namespace spot
 	    // Accumulate all acceptance conditions into the
 	    // merged SCC.
 	    ecs_->root.top().condition |= acc;
+	    ecs_->root.rem().splice(ecs_->root.rem().end(), rem);
 
 	    // Have we found all acceptance conditions?
 	    if (ecs_->root.top().condition
@@ -453,7 +496,7 @@ namespace spot
 	    // Group the pending successors of formed SCC if requested.
 	    if (group_)
 	      {
-		assert(todo.back().s != 0);
+		assert(todo.back().s);
 		while (ecs_->root.top().index < todo.back().n)
 		  {
 		    todo_list::reverse_iterator prev = todo.rbegin();
@@ -464,8 +507,21 @@ namespace spot
 			merged = true;
 		      }
 		    prev->q.splice(prev->q.end(), last->q);
+
+		    if (poprem_)
+		      {
+			numbered_state_heap::state_index_p spi =
+			  ecs_->h->index(todo.back().s);
+			assert(spi.first);
+			ecs_->root.rem().push_front(spi.first);
+			// Don't change the stack depth, since
+			// we are just moving the state from TODO to REM.
+		      }
+		    else
+		      {
+			dec_depth();
+		      }
 		    todo.pop_back();
-		    // dec_depth();
 		  }
 		new_queue = &todo.back().q;
 	      }
diff --git a/src/tgbaalgos/gtec/gtec.hh b/src/tgbaalgos/gtec/gtec.hh
index c65435ce6..594296b17 100644
--- a/src/tgbaalgos/gtec/gtec.hh
+++ b/src/tgbaalgos/gtec/gtec.hh
@@ -1,4 +1,4 @@
-// Copyright (C) 2003, 2004  Laboratoire d'Informatique de Paris 6 (LIP6),
+// Copyright (C) 2003, 2004, 2005  Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
 // et Marie Curie.
 //
@@ -22,6 +22,7 @@
 #ifndef SPOT_TGBAALGOS_GTEC_GTEC_HH
 # define SPOT_TGBAALGOS_GTEC_GTEC_HH
 
+#include <stack>
 #include "status.hh"
 #include "tgbaalgos/emptiness.hh"
 #include "tgbaalgos/emptiness_stats.hh"
@@ -76,6 +77,7 @@ namespace spot
   {
   public:
     couvreur99_check(const tgba* a,
+		     bool poprem = true,
 		     const numbered_state_heap_factory* nshf
 		     = numbered_state_heap_hash_map_factory::instance());
     virtual ~couvreur99_check();
@@ -103,6 +105,9 @@ namespace spot
     /// state. In other words, it removes the strongly connected
     /// component that contains this state.
     void remove_component(const state* start_delete);
+
+    /// Whether to store the state to be removed.
+    bool poprem_;
   };
 
   /// \brief A version of spot::couvreur99_check that tries to visit
@@ -118,6 +123,7 @@ namespace spot
   {
   public:
     couvreur99_check_shy(const tgba* a,
+			 bool poprem = true,
 			 bool group = true,
 			 const numbered_state_heap_factory* nshf
 			 = numbered_state_heap_hash_map_factory::instance());
@@ -144,7 +150,6 @@ namespace spot
     // * todo, the depth-first search stack.  This holds pairs of the
     //   form (STATE, SUCCESSORS) where SUCCESSORS is a list of
     //   (ACCEPTANCE_CONDITIONS, STATE) pairs.
-
     typedef std::list<successor> succ_queue;
 
     struct todo_item
diff --git a/src/tgbaalgos/gtec/sccstack.cc b/src/tgbaalgos/gtec/sccstack.cc
index 6a26d8a6e..aef399679 100644
--- a/src/tgbaalgos/gtec/sccstack.cc
+++ b/src/tgbaalgos/gtec/sccstack.cc
@@ -1,4 +1,4 @@
-// Copyright (C) 2004  Laboratoire d'Informatique de Paris 6 (LIP6),
+// Copyright (C) 2004, 2005  Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
 // et Marie Curie.
 //
@@ -32,21 +32,35 @@ namespace spot
   scc_stack::connected_component&
   scc_stack::top()
   {
-    return s.top();
+    return s.front();
+  }
+
+  const scc_stack::connected_component&
+  scc_stack::top() const
+  {
+    return s.front();
   }
 
   void
   scc_stack::pop()
   {
-    s.pop();
+    // assert(rem().empty());
+    s.pop_front();
   }
 
   void
   scc_stack::push(int index)
   {
-    s.push(connected_component(index));
+    s.push_front(connected_component(index));
   }
 
+  std::list<const state*>&
+  scc_stack::rem()
+  {
+    return top().rem;
+  }
+
+
   size_t
   scc_stack::size() const
   {
@@ -58,4 +72,18 @@ namespace spot
   {
     return s.empty();
   }
+
+  unsigned
+  scc_stack::clear_rem()
+  {
+    unsigned n = 0;
+    for (stack_type::iterator i = s.begin(); i != s.end(); ++i)
+      {
+	n += i->rem.size();
+	i->rem.clear();
+      }
+    return n;
+  }
+
+
 }
diff --git a/src/tgbaalgos/gtec/sccstack.hh b/src/tgbaalgos/gtec/sccstack.hh
index 1d8708365..56d50c240 100644
--- a/src/tgbaalgos/gtec/sccstack.hh
+++ b/src/tgbaalgos/gtec/sccstack.hh
@@ -1,4 +1,4 @@
-// Copyright (C) 2004  Laboratoire d'Informatique de Paris 6 (LIP6),
+// Copyright (C) 2004, 2005  Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
 // et Marie Curie.
 //
@@ -22,8 +22,9 @@
 #ifndef SPOT_TGBAALGOS_GTEC_SCCSTACK_HH
 # define SPOT_TGBAALGOS_GTEC_SCCSTACK_HH
 
-#include <stack>
 #include <bdd.h>
+#include <list>
+#include <tgba/state.hh>
 
 namespace spot
 {
@@ -42,6 +43,8 @@ namespace spot
       /// The bdd condition is the union of all acceptance conditions of
       /// transitions which connect the states of the connected component.
       bdd condition;
+
+      std::list<const state*> rem;
     };
 
     /// Stack a new SCC with index \a index.
@@ -50,16 +53,27 @@ namespace spot
     /// Access the top SCC.
     connected_component& top();
 
+    /// Access the top SCC.
+    const connected_component& top() const;
+
     /// Pop the top SCC.
     void pop();
 
     /// How many SCC are in stack.
     size_t size() const;
 
+    /// The \c rem member of the top SCC.
+    std::list<const state*>& rem();
+
+    /// Purge all \c rem members.
+    ///
+    /// \return the number of elements cleared.
+    unsigned clear_rem();
+
     /// Is the stack empty?
     bool empty() const;
 
-    typedef std::stack<connected_component> stack_type;
+    typedef std::list<connected_component> stack_type;
     stack_type s;
   };
 }
diff --git a/src/tgbatest/ltl2tgba.cc b/src/tgbatest/ltl2tgba.cc
index cf6854e71..a71f856b9 100644
--- a/src/tgbatest/ltl2tgba.cc
+++ b/src/tgbatest/ltl2tgba.cc
@@ -136,6 +136,9 @@ syntax(char* prog)
 	    << "  Cou99 (the default)" << std::endl
 	    << "  Cou99_shy-" << std::endl
 	    << "  Cou99_shy" << std::endl
+	    << "  Cou99_rem" << std::endl
+	    << "  Cou99_rem_shy-" << std::endl
+	    << "  Cou99_rem_shy" << std::endl
 	    << "  CVWY90" << std::endl
 	    << "  CVWY90_repeated" << std::endl
 	    << "  CVWY90_bsh[(heap size in Mo - 10Mo by default)]"
@@ -174,6 +177,7 @@ main(int argc, char** argv)
 	 Tau03Search, Tau03OptSearch, Gv04 } echeck = None;
   enum { NoneDup, BFS, DFS } dupexp = NoneDup;
   bool couv_group = true;
+  bool poprem = false;
   bool search_many = false;
   bool bit_state_hashing = false;
   int heap_size = 10*1024*1024;
@@ -426,6 +430,23 @@ main(int argc, char** argv)
 	  echeck = Couvreur2;
 	  couv_group = false;
 	}
+      else if (echeck_algo == "Cou99_rem")
+	{
+	  echeck = Couvreur;
+	  poprem = true;
+	}
+      else if (echeck_algo == "Cou99_rem_shy")
+	{
+	  echeck = Couvreur2;
+	  couv_group = true;
+	  poprem = true;
+	}
+      else if (echeck_algo == "Cou99_rem_shy-")
+	{
+	  echeck = Couvreur2;
+	  couv_group = false;
+	  poprem = true;
+	}
       else if (echeck_algo == "CVWY90")
 	{
 	  echeck = MagicSearch;
@@ -728,11 +749,11 @@ main(int argc, char** argv)
 	  break;
 
 	case Couvreur:
-	  ec = new spot::couvreur99_check(a);
+	  ec = new spot::couvreur99_check(a, poprem);
 	  break;
 
 	case Couvreur2:
-	  ec = new spot::couvreur99_check_shy(a, couv_group);
+	  ec = new spot::couvreur99_check_shy(a, poprem, couv_group);
 	  break;
 
         case MagicSearch:
diff --git a/src/tgbatest/randtgba.cc b/src/tgbatest/randtgba.cc
index 0a6748069..7bd295499 100644
--- a/src/tgbatest/randtgba.cc
+++ b/src/tgbatest/randtgba.cc
@@ -65,19 +65,37 @@
 spot::emptiness_check*
 couvreur99_cons(const spot::tgba* a)
 {
-  return new spot::couvreur99_check(a);
+  return new spot::couvreur99_check(a, false);
 }
 
 spot::emptiness_check*
 couvreur99_shy_cons(const spot::tgba* a)
 {
-  return new spot::couvreur99_check_shy(a);
+  return new spot::couvreur99_check_shy(a, false);
 }
 
 spot::emptiness_check*
 couvreur99_shy_minus_cons(const spot::tgba* a)
 {
-  return new spot::couvreur99_check_shy(a, false);
+  return new spot::couvreur99_check_shy(a, false, false);
+}
+
+spot::emptiness_check*
+couvreur99_rem_cons(const spot::tgba* a)
+{
+  return new spot::couvreur99_check(a, true);
+}
+
+spot::emptiness_check*
+couvreur99_rem_shy_cons(const spot::tgba* a)
+{
+  return new spot::couvreur99_check_shy(a, true);
+}
+
+spot::emptiness_check*
+couvreur99_rem_shy_minus_cons(const spot::tgba* a)
+{
+  return new spot::couvreur99_check_shy(a, true, false);
 }
 
 spot::emptiness_check*
@@ -103,16 +121,19 @@ struct ec_algo
 
 ec_algo ec_algos[] =
   {
-    { "Cou99",      couvreur99_cons,                 0, -1U, true },
-    { "Cou99_shy-", couvreur99_shy_minus_cons,       0, -1U, true },
-    { "Cou99_shy",  couvreur99_shy_cons,             0, -1U, true },
-    { "CVWY90",     spot::explicit_magic_search,     0,   1, true },
-    { "CVWY90_bsh", bsh_ms_cons,                     0,   1, false },
-    { "GV04",       spot::explicit_gv04_check,       0,   1, true },
-    { "SE05",       spot::explicit_se05_search,      0,   1, true },
-    { "SE05_bsh",   bsh_se05_cons,                   0,   1, false },
-    { "Tau03",      spot::explicit_tau03_search,     1, -1U, true },
-    { "Tau03_opt",  spot::explicit_tau03_opt_search, 0, -1U, true },
+    { "Cou99",          couvreur99_cons,                     0, -1U, true },
+    { "Cou99_shy-",     couvreur99_shy_minus_cons,           0, -1U, true },
+    { "Cou99_shy",      couvreur99_shy_cons,                 0, -1U, true },
+    { "Cou99_rem",      couvreur99_rem_cons,                 0, -1U, true },
+    { "Cou99_rem_shy-", couvreur99_rem_shy_minus_cons,       0, -1U, true },
+    { "Cou99_rem_shy",  couvreur99_rem_shy_cons,             0, -1U, true },
+    { "CVWY90",         spot::explicit_magic_search,         0,   1, true },
+    { "CVWY90_bsh",     bsh_ms_cons,                         0,   1, false },
+    { "GV04",           spot::explicit_gv04_check,           0,   1, true },
+    { "SE05",           spot::explicit_se05_search,          0,   1, true },
+    { "SE05_bsh",       bsh_se05_cons,                       0,   1, false },
+    { "Tau03",          spot::explicit_tau03_search,         1, -1U, true },
+    { "Tau03_opt",      spot::explicit_tau03_opt_search,     0, -1U, true },
   };
 
 spot::emptiness_check*