diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h
index ba4d2cc724f..3f6f50b23aa 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse.h
@@ -66,7 +66,7 @@ public:
   
   typedef EdgeCollapse Self ;
   
-  typedef undirected_graph_traits<TSM>       UndirectedGraphTraits ;  // This is a CGAL extension. Is not in boost
+  typedef halfedge_graph_traits<TSM>         HalfedgeGraphTraits ;  // This is a CGAL extension. Is not in boost
   typedef boost::graph_traits    <TSM>       GraphTraits ;
   typedef boost::graph_traits    <TSM const> ConstGraphTraits ;
   
@@ -82,7 +82,7 @@ public:
   typedef typename ConstGraphTraits::vertex_descriptor const_vertex_descriptor ;
   typedef typename ConstGraphTraits::edge_descriptor   const_edge_descriptor ;
   
-  typedef typename UndirectedGraphTraits::edge_iterator undirected_edge_iterator ;
+  typedef typename HalfedgeGraphTraits::undirected_edge_iterator undirected_edge_iterator ;
 
   typedef typename GetCost     ::result_type Optional_cost_type ;
   typedef typename GetPlacement::result_type Optional_placement_type ;
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse_impl.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse_impl.h
index efe1d203e9e..50cf86e5bc2 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse_impl.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/Edge_collapse_impl.h
@@ -100,7 +100,7 @@ void EdgeCollapse<M,S,X,F,D,CF,PF,CP,PP,V>::Collect()
   
   Equal_3 equal_points = Kernel().equal_3_object();
     
-  size_type lSize = num_undirected_edges(mSurface) ;
+  size_type lSize = num_edges(mSurface) / 2 ;
   
   mInitialEdgeCount = mCurrentEdgeCount = lSize;
   
diff --git a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/TSMS_common.h b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/TSMS_common.h
index 0aabaa2fdf4..0780633b9e2 100644
--- a/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/TSMS_common.h
+++ b/Surface_mesh_simplification/include/CGAL/Surface_mesh_simplification/Detail/TSMS_common.h
@@ -74,16 +74,6 @@ bool handle_exists ( Iterator begin, Iterator end, Handle h )
  return false ;
 }
 
-template<class TSM> 
-struct Surface_geometric_traits
-{ 
-  typedef typename TSM::Point_3 Point_3 ;
-  
-  typedef typename Kernel_traits<Point_3>::Kernel Kernel ;
-  
-  typedef typename Kernel::FT FT ;
-  
-} ;
 
 template<class T, class U> struct ChooseNotVoidType ;
 template<class T>          struct ChooseNotVoidType<T   ,void> { typedef T    type ; } ;