diff --git a/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3_refinement_visitor.h b/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3_refinement_visitor.h
index ed843914bff..394613c1d81 100644
--- a/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3_refinement_visitor.h
+++ b/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3_refinement_visitor.h
@@ -793,9 +793,11 @@ public:
                 #endif
               }
               std::pair<int,int> edge_pair(*it_id,node_id_of_first);
-              border_halfedges.insert( std::make_pair(hedge,edge_pair) );
-              put(m_edge_mark_pmap,std::make_pair(hedge,poly),true);
-              put(m_edge_mark_pmap,std::make_pair(hedge->opposite(),poly),true);
+              if ( border_halfedges.insert( std::make_pair(hedge,edge_pair) ).second)
+              {
+                put(m_edge_mark_pmap,std::make_pair(hedge,poly),true);
+                put(m_edge_mark_pmap,std::make_pair(hedge->opposite(),poly),true);
+              }
               update_edge_per_polyline(poly,edge_pair,hedge); 
               //save the fact that we already handle this edge
               already_done.insert(std::make_pair(node_id_of_first,*it_id));
@@ -1102,9 +1104,11 @@ public:
         //is defined as one of them defines an adjacent face
         //CGAL_assertion(it_poly_hedge!=edge_to_hedge.end());
         if( it_poly_hedge!=edge_to_hedge.end() ){
-          border_halfedges.insert( std::make_pair(Halfedge_const_handle(it_poly_hedge->second),*it_cst) );
-          put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second,P),true);
-          put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second->opposite(),P),true); //setting the opposite is only needed for border edges (done in adjacent triangle otherwise)
+          if ( border_halfedges.insert( std::make_pair(Halfedge_const_handle(it_poly_hedge->second),*it_cst) ).second)
+          {
+            put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second,P),true);
+            put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second->opposite(),P),true); //setting the opposite is only needed for border edges (done in adjacent triangle otherwise)
+          }
           update_edge_per_polyline(P,it_poly_hedge->first,it_poly_hedge->second);
         }
         else{
@@ -1114,9 +1118,11 @@ public:
           it_poly_hedge=edge_to_hedge.find(opposite_pair);
           CGAL_assertion( it_poly_hedge!=edge_to_hedge.end() );
 
-          border_halfedges.insert( std::make_pair(Halfedge_const_handle(it_poly_hedge->second),opposite_pair) );
-          put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second,P),true);
-          put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second->opposite(),P),true); //setting the opposite is only needed for border edges (done in adjacent triangle otherwise)
+          if ( border_halfedges.insert( std::make_pair(Halfedge_const_handle(it_poly_hedge->second),opposite_pair) ).second )
+          {
+            put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second,P),true);
+            put(m_edge_mark_pmap,std::make_pair(it_poly_hedge->second->opposite(),P),true); //setting the opposite is only needed for border edges (done in adjacent triangle otherwise)
+          }
           update_edge_per_polyline(P,it_poly_hedge->first,it_poly_hedge->second);          
         }
       }