diff --git a/NEWS b/NEWS
index 6961859db..d0a637131 100644
--- a/NEWS
+++ b/NEWS
@@ -24,6 +24,12 @@ New in spot 1.1a (not yet released):
       Some illustrations of this point and the previous one can be
       found in the man page for ltl2tgba(1).
 
+    - There is a new function scc_filter_states() that removes all
+      useless states from a TGBA.  It is actually an abbridged version
+      of scc_filter() that does not alter the acceptance conditions of
+      the automaton.  scc_filter_state() should be used when
+      post-processing TGBAs that actually represent BAs.
+
   * Bug fixes:
 
     - genltl --gh-r generated the wrong formulas due to a typo.
diff --git a/src/tgbaalgos/postproc.cc b/src/tgbaalgos/postproc.cc
index 5c77324e8..0d636c915 100644
--- a/src/tgbaalgos/postproc.cc
+++ b/src/tgbaalgos/postproc.cc
@@ -110,12 +110,20 @@ namespace spot
       scc_filter_ = 1;
 
     // Remove useless SCCs.
-    if (scc_filter_ > 0 || type_ == Monitor)
-    {
-      const tgba* s = scc_filter(a, scc_filter_ > 1);
-      delete a;
-      a = s;
-    }
+    if (type_ == Monitor)
+      {
+	// Do not bother about acceptance conditions, they we be
+	// ignored.
+	const tgba* s = scc_filter_states(a);
+	delete a;
+	a = s;
+      }
+    else if (scc_filter_ > 0)
+      {
+	const tgba* s = scc_filter(a, scc_filter_ > 1);
+	delete a;
+	a = s;
+      }
 
     if (type_ == Monitor)
       {
diff --git a/src/tgbaalgos/sccfilter.cc b/src/tgbaalgos/sccfilter.cc
index ee5a2e4ac..ae8f0cc72 100644
--- a/src/tgbaalgos/sccfilter.cc
+++ b/src/tgbaalgos/sccfilter.cc
@@ -65,6 +65,53 @@ namespace spot
       return out_aut->create_transition(in_f, out_f);
     }
 
+    template<class T>
+    class filter_iter_states: public tgba_reachable_iterator_depth_first
+    {
+    public:
+      typedef T output_t;
+
+      filter_iter_states(const tgba* a,
+			 const scc_map& sm,
+			 const std::vector<bool>& useless)
+	: tgba_reachable_iterator_depth_first(a),
+	  out_(new T(a->get_dict())),
+	  sm_(sm),
+	  useless_(useless)
+      {
+	a->get_dict()->register_all_variables_of(a, out_);
+	out_->set_acceptance_conditions(a->all_acceptance_conditions());
+      }
+
+      T*
+      result()
+      {
+	return out_;
+      }
+
+      bool
+      want_state(const state* s) const
+      {
+	return !useless_[sm_.scc_of_state(s)];
+      }
+
+      void
+      process_link(const state* in_s, int in,
+		   const state* out_s, int out,
+		   const tgba_succ_iterator* si)
+      {
+	typename output_t::state::transition* t =
+	  create_transition(this->aut_, out_, in_s, in, out_s, out);
+	t->condition = si->current_condition();
+	t->acceptance_conditions = si->current_acceptance_conditions();
+      }
+
+    protected:
+      T* out_;
+      const scc_map& sm_;
+      const std::vector<bool>& useless_;
+    };
+
     template<class T>
     class filter_iter: public tgba_reachable_iterator_depth_first
     {
@@ -495,4 +542,55 @@ namespace spot
     return ret;
   }
 
+  tgba* scc_filter_states(const tgba* aut, scc_map* given_sm)
+  {
+    scc_map* sm = given_sm;
+    if (!sm)
+      {
+	sm = new scc_map(aut);
+	sm->build_map();
+      }
+    scc_stats ss = build_scc_stats(*sm);
+
+    tgba* ret;
+
+    const tgba_explicit_formula* af =
+      dynamic_cast<const tgba_explicit_formula*>(aut);
+    if (af)
+      {
+	filter_iter_states<tgba_explicit_formula> fi(af, *sm,
+						     ss.useless_scc_map);
+	fi.run();
+	tgba_explicit_formula* res = fi.result();
+	res->merge_transitions();
+	ret = res;
+      }
+    else
+      {
+	const tgba_explicit_string* as =
+	  dynamic_cast<const tgba_explicit_string*>(aut);
+	if (as)
+	  {
+	    filter_iter_states<tgba_explicit_string> fi(aut, *sm,
+							ss.useless_scc_map);
+	    fi.run();
+	    tgba_explicit_string* res = fi.result();
+	    res->merge_transitions();
+	    ret = res;
+	  }
+	else
+	  {
+	    filter_iter_states<tgba_explicit_number> fi(aut, *sm,
+							ss.useless_scc_map);
+	    fi.run();
+	    tgba_explicit_number* res = fi.result();
+	    res->merge_transitions();
+	    ret = res;
+	  }
+      }
+    if (!given_sm)
+      delete sm;
+    return ret;
+  }
+
 }
diff --git a/src/tgbaalgos/sccfilter.hh b/src/tgbaalgos/sccfilter.hh
index 791d04052..04f2167b9 100644
--- a/src/tgbaalgos/sccfilter.hh
+++ b/src/tgbaalgos/sccfilter.hh
@@ -1,4 +1,4 @@
-// Copyright (C) 2009, 2010, 2012 Laboratoire de Recherche et
+// Copyright (C) 2009, 2010, 2012, 2013 Laboratoire de Recherche et
 // Developpement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -56,10 +56,24 @@ namespace spot
   /// variable are also removed from transitions entering an accepting
   /// SCC.  ignored is a conjunction of positive variables that should
   /// be removed everywhere.
+  ///
+  /// \warning Calling scc_filter on a TGBA that has the SBA property
+  /// (i.e., transitions leaving accepting states are all marked as
+  /// accepting) may destroy this property.  Use scc_filter_states()
+  /// instead.
   tgba* scc_filter(const tgba* aut, bool remove_all_useless = false,
 		   scc_map* given_sm = 0, bdd susp = bddtrue,
 		   bool early_susp = false, bdd ignored = bddtrue);
 
+  /// \brief Prune unaccepting SCCs.
+  ///
+  /// This is an abridged version of scc_filter(), that only remove
+  /// useless states, without touching at the acceptance conditions.
+  ///
+  /// Especially, if the input TGBA has the SBA property, (i.e.,
+  /// transitions leaving accepting states are all marked as
+  /// accepting), then the output TGBA will also have that property.
+  tgba* scc_filter_states(const tgba* aut, scc_map* given_sm = 0);
 }
 
 #endif // SPOT_TGBAALGOS_SCC_HH