diff --git a/include/Algo/ImplicitHierarchicalMesh/ihm.hpp b/include/Algo/ImplicitHierarchicalMesh/ihm.hpp
index 4f8e26ef557116a197fc6661cbfa62329dd64d56..12b4a85557c2d963defb166d42e90b1490ed31cb 100644
--- a/include/Algo/ImplicitHierarchicalMesh/ihm.hpp
+++ b/include/Algo/ImplicitHierarchicalMesh/ihm.hpp
@@ -347,11 +347,10 @@ T& AttributeHandler_IHM<T>::operator[](Dart d)
 	unsigned int nbSteps = m->m_curLevel - m->vertexInsertionLevel(d) ;
 	unsigned int index = m->getEmbedding(d, orbit) ;
 
-	if(index == EMBNULL && nbSteps == 0)
+	if(index == EMBNULL)
 	{
 		index = m->embedNewCell(orbit, d) ;
 		m->m_nextLevelCell[orbit]->operator[](index) = EMBNULL ;
-		return this->m_attrib->operator[](index);
 	}
 
 	AttributeContainer& cont = m->getAttributeContainer(orbit) ;
diff --git a/include/Algo/ImplicitHierarchicalMesh/subdivision.hpp b/include/Algo/ImplicitHierarchicalMesh/subdivision.hpp
index 9cbe9ccc53f7aaac741649911e353fdea48b1940..0d3df5930d0c3a79da73561dc62c49d320d1fa6a 100644
--- a/include/Algo/ImplicitHierarchicalMesh/subdivision.hpp
+++ b/include/Algo/ImplicitHierarchicalMesh/subdivision.hpp
@@ -162,13 +162,39 @@ void coarsenFace(typename PFP::MAP& map, Dart d, typename PFP::TVEC3& position)
 	assert(map.faceIsSubdividedOnce(d) || !"Trying to coarsen a non-subdivided face or a more than once subdivided face") ;
 
 	unsigned int cur = map.getCurrentLevel() ;
-	map.setCurrentLevel(cur + 1) ;
-	Dart cv = map.phi1(map.phi1(d)) ;
-	map.setCurrentLevel(map.getMaxLevel()) ;
-	map.deleteVertex(cv) ;
-	map.setCurrentLevel(cur) ;
+
+	unsigned int degree = 0 ;
 	Dart fit = d ;
 	do
+	{
+		++degree ;
+		fit = map.phi1(fit) ;
+	} while(fit != d) ;
+
+	if(degree == 3)
+	{
+		fit = d ;
+		do
+		{
+			map.setCurrentLevel(cur + 1) ;
+			Dart innerEdge = map.phi1(fit) ;
+			map.setCurrentLevel(map.getMaxLevel()) ;
+			map.mergeFaces(innerEdge) ;
+			map.setCurrentLevel(cur) ;
+			fit = map.phi1(fit) ;
+		} while(fit != d) ;
+	}
+	else
+	{
+		map.setCurrentLevel(cur + 1) ;
+		Dart centralV = map.phi1(map.phi1(d)) ;
+		map.setCurrentLevel(map.getMaxLevel()) ;
+		map.deleteVertex(centralV) ;
+		map.setCurrentLevel(cur) ;
+	}
+
+	fit = d ;
+	do
 	{
 		if(map.edgeCanBeCoarsened(fit))
 			coarsenEdge<PFP>(map, fit, position) ;
diff --git a/include/Topology/generic/embeddedMap2.hpp b/include/Topology/generic/embeddedMap2.hpp
index 722a7d4465dae8ec6b19cdd040772f75f5119f34..4fbfa68dd0d53489f0b837c477913ee8f3dd3286 100644
--- a/include/Topology/generic/embeddedMap2.hpp
+++ b/include/Topology/generic/embeddedMap2.hpp
@@ -397,17 +397,31 @@ template <typename MAP2>
 bool EmbeddedMap2<MAP2>::mergeFaces(Dart d)
 {
 	Dart dNext = MAP2::phi1(d) ;
+	Dart e = MAP2::phi2(d) ;
+	Dart eNext = MAP2::phi1(e) ;
 
+	unsigned int vEmb1 = EMBNULL ;
+	unsigned int vEmb2 = EMBNULL ;
+	if(MAP2::isOrbitEmbedded(VERTEX_ORBIT))
+	{
+		vEmb1 = MAP2::getDartEmbedding(VERTEX_ORBIT, d) ;
+		vEmb2 = MAP2::getDartEmbedding(VERTEX_ORBIT, e) ;
+	}
 	unsigned int fEmb = EMBNULL ;
 	if (MAP2::isOrbitEmbedded(FACE_ORBIT))
 	{
 		fEmb = MAP2::getEmbedding(d, FACE_ORBIT) ;
-		if(fEmb != EMBNULL)
-			MAP2::setDartEmbedding(FACE_ORBIT, dNext, fEmb) ;
 	}
 
 	if(MAP2::mergeFaces(d))
 	{
+		if (MAP2::isOrbitEmbedded(VERTEX_ORBIT))
+		{
+			if(vEmb1 != EMBNULL)
+				MAP2::setDartEmbedding(VERTEX_ORBIT, eNext, vEmb1) ;
+			if(vEmb2 != EMBNULL)
+				MAP2::setDartEmbedding(VERTEX_ORBIT, dNext, vEmb2) ;
+		}
 		if (MAP2::isOrbitEmbedded(FACE_ORBIT))
 		{
 			MAP2::embedOrbit(FACE_ORBIT, dNext, fEmb) ;
diff --git a/src/Algo/ImplicitHierarchicalMesh/ihm.cpp b/src/Algo/ImplicitHierarchicalMesh/ihm.cpp
index 95434c7374230bdef5812399c47b31856f19fef3..520a2ec81f0c2ee6e3b8f6b0715f39a7c1298318 100644
--- a/src/Algo/ImplicitHierarchicalMesh/ihm.cpp
+++ b/src/Algo/ImplicitHierarchicalMesh/ihm.cpp
@@ -284,7 +284,7 @@ bool ImplicitHierarchicalMap::faceIsSubdividedOnce(Dart d)
 		++m_curLevel ;
 		Dart cf = phi2(phi1(d)) ;
 		++m_curLevel ;
-		if(m_dartLevel[phi1(d)] == m_curLevel && m_edgeId[phi1(d)] != m_edgeId[d])
+		if(m_dartLevel[phi1(cf)] == m_curLevel && m_edgeId[phi1(cf)] != m_edgeId[cf])
 			subdOnce = false ;
 		--m_curLevel ;
 		--m_curLevel ;