diff --git a/include/Topology/generic/genericmap.h b/include/Topology/generic/genericmap.h
index 32c669e59d4806ec3cd14ddf54dea2dc3891b6ff..9ed29a269e62d984336a9ab11186847d76271b3d 100644
--- a/include/Topology/generic/genericmap.h
+++ b/include/Topology/generic/genericmap.h
@@ -447,7 +447,7 @@ public:
 	void enableQuickTraversal() ;
 
 	template <unsigned int ORBIT>
-	void updateQuickTraversal() ;
+	void updateQuickTraversal(const FunctorSelect& good = allDarts) ;
 
 	template <unsigned int ORBIT>
 	AttributeMultiVector<Dart>* getQuickTraversal() ;
diff --git a/include/Topology/generic/genericmap.hpp b/include/Topology/generic/genericmap.hpp
index 231c21e5f5dc44e8e055d53063f4a4a90ed13e71..130ef8ed5851e0159f9e1801d4ebd13274954831 100644
--- a/include/Topology/generic/genericmap.hpp
+++ b/include/Topology/generic/genericmap.hpp
@@ -435,14 +435,14 @@ inline void GenericMap::enableQuickTraversal()
 }
 
 template <unsigned int ORBIT>
-inline void GenericMap::updateQuickTraversal()
+inline void GenericMap::updateQuickTraversal(const FunctorSelect& good)
 {
 	assert(m_quickTraversal[ORBIT] != NULL || !"updateQuickTraversal on a disabled orbit") ;
 
 	CellMarker<ORBIT> cm(*this) ;
 	for(Dart d = begin(); d != end(); next(d))
 	{
-		if(!cm.isMarked(d))
+		if(good(d) && !cm.isMarked(d))
 		{
 			cm.mark(d) ;
 			(*m_quickTraversal[ORBIT])[getEmbedding<ORBIT>(d)] = d ;
diff --git a/include/Topology/generic/traversorCell.hpp b/include/Topology/generic/traversorCell.hpp
index 62c68f2b060f203b338cf99360882aa9451eb26a..18d492c399432bc010370672948e5eb30197ed8a 100644
--- a/include/Topology/generic/traversorCell.hpp
+++ b/include/Topology/generic/traversorCell.hpp
@@ -29,30 +29,32 @@ template <typename MAP, unsigned int ORBIT>
 TraversorCell<MAP, ORBIT>::TraversorCell(MAP& map, const FunctorSelect& good, bool forceDartMarker, unsigned int thread) :
 	m(map), dmark(NULL), cmark(NULL), current(NIL), firstTraversal(true), m_good(good)
 {
-	quickTraversal = map.template getQuickTraversal<ORBIT>() ;
-	if(quickTraversal != NULL)
-	{
-		cont = &(m.template getAttributeContainer<ORBIT>()) ;
-	}
+	if(forceDartMarker)
+		dmark = new DartMarker(map, thread) ;
 	else
 	{
-		if(!forceDartMarker && map.template isOrbitEmbedded<ORBIT>())
-			cmark = new CellMarker<ORBIT>(map, thread) ;
+		quickTraversal = map.template getQuickTraversal<ORBIT>() ;
+		if(quickTraversal != NULL)
+		{
+			cont = &(m.template getAttributeContainer<ORBIT>()) ;
+		}
 		else
-			dmark = new DartMarker(map, thread) ;
+		{
+			if(map.template isOrbitEmbedded<ORBIT>())
+				cmark = new CellMarker<ORBIT>(map, thread) ;
+			else
+				dmark = new DartMarker(map, thread) ;
+		}
 	}
 }
 
 template <typename MAP, unsigned int ORBIT>
 TraversorCell<MAP, ORBIT>::~TraversorCell()
 {
-	if(quickTraversal == NULL)
-	{
-		if(dmark)
-			delete dmark ;
-		else
-			delete cmark ;
-	}
+	if(dmark)
+		delete dmark ;
+	else if(cmark)
+		delete cmark ;
 }
 
 template <typename MAP, unsigned int ORBIT>