diff --git a/Point_set_2/include/CGAL/Point_set_2.h b/Point_set_2/include/CGAL/Point_set_2.h
index 443b286e579..6bf41ac1be6 100644
--- a/Point_set_2/include/CGAL/Point_set_2.h
+++ b/Point_set_2/include/CGAL/Point_set_2.h
@@ -250,7 +250,7 @@ public:
      Point p = v->point();
      
      // "unmark" the vertices ...
-     init_dfs();
+     init_search();
 
      MAP_TYPE                                        priority_number;              // here we save the priorities ...
      internal::compare_vertices<Vertex_handle,Numb_type,MAP_TYPE>    
@@ -293,7 +293,6 @@ public:
   } 
    
    
-  // dfs
   // for marking nodes in search procedures
   size_type cur_mark;
    
@@ -305,7 +304,7 @@ public:
      mark.clear();
   }
   
-  void init_dfs()
+  void init_search()
   {
      cur_mark++; 
      if (cur_mark == (std::numeric_limits<size_type>::max)()) init_vertex_marks();
@@ -324,7 +323,7 @@ public:
     return (mark[vh] == cur_mark);
   }
   
-  void dfs(Vertex_handle v,const Circle& C, std::list<Vertex_handle>& L)
+  void search(Vertex_handle v,const Circle& C, std::list<Vertex_handle>& L)
   {
     std::stack<Vertex_handle> todo;
     todo.push(v);
@@ -385,10 +384,10 @@ public:
        v = insert(p); 
      }
      
-     init_dfs();
+     init_search();
      
      std::list<Vertex_handle> L;
-     dfs(v,C,L);
+     search(v,C,L);
      
      if (new_v)
      { L.pop_front();   //first one was inserted in range_search ...