diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_dcel_base.h b/Arrangement_on_surface_2/include/CGAL/Arr_dcel_base.h
index 04a54c430fe..0b9f1d54cae 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_dcel_base.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_dcel_base.h
@@ -516,10 +516,10 @@ public:
   typedef Inner_ccb                    Hole;
 
 private:
-  typedef Cast_function_object<void*, Halfedge*>        _Ccb_to_halfedge_cast;
-  // typedef Cast_function_object<const void*,
-  //                              const Halfedge*>  _Const_ccb_to_halfedge_cast;
-  typedef _Ccb_to_halfedge_cast _Const_ccb_to_halfedge_cast;
+  typedef Cast_function_object<void*, Halfedge*> _Ccb_to_halfedge_cast;
+  // typedef Cast_function_object<const void*, const Halfedge*>
+  //                                             _Const_ccb_to_halfedge_cast;
+  typedef _Ccb_to_halfedge_cast                  _Const_ccb_to_halfedge_cast;
 
 public:
 
@@ -667,6 +667,26 @@ public:
   /*! Erase an isloated vertex from the face. */
   void erase_isolated_vertex(Isolated_vertex *iv)
   { this->iso_verts.erase(iv->iterator().current_iterator()); }
+
+  /*! Move all isolated vertices from the face to another. */
+  Isolated_vertex_iterator splice_isolated_vertices(Arr_face& other)
+  {
+    const bool was_empty = this->iso_verts.empty();
+    typename Base::Isolated_vertices_container::iterator previous =
+      this->iso_verts.end();
+    if (!was_empty) --previous;
+    this->iso_verts.splice(this->iso_verts.end(), other.iso_verts);
+    if (was_empty) previous = this->iso_verts.begin();
+    else ++previous;
+    for (typename Base::Isolated_vertices_container::iterator it = previous;
+         it != this->iso_verts.end(); ++it)
+    {
+      Isolated_vertex* iv = static_cast<Vertex*>(*it)->isolated_vertex();
+      iv->set_iterator(it);
+      iv->set_face(this);
+    }
+    return previous;
+  }
 };
 
 /*! \class
diff --git a/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h b/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h
index 475f2367bd6..6b3b4805241 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h
@@ -2095,6 +2095,33 @@ _move_isolated_vertex(DFace* from_face, DFace* to_face, DVertex* v)
   _notify_after_move_isolated_vertex(vh);
 }
 
+//-----------------------------------------------------------------------------
+// Move all isolated vertices from one face to another.
+//
+template <typename GeomTraits, typename TopTraits>
+void Arrangement_on_surface_2<GeomTraits, TopTraits>::
+_move_all_isolated_vertices(DFace* from_face, DFace* to_face)
+{
+  // Comment EFEF 2015-09-28: The following loop and the loop at the end of this
+  // function should be replaced with a pair of notifiers, respectively,
+  // function_notify_before_move_all_isolated_vertices();
+  // function_notify_after_move_all_isolated_vertices();
+  DIso_vertex_iter iv_it = from_face->isolated_vertices_begin();
+  while (iv_it != from_face->isolated_vertices_end()) {
+    DVertex* v = &(*iv_it++);
+    Vertex_handle vh(v);
+    _notify_before_move_isolated_vertex(Face_handle(from_face),
+                                        Face_handle(to_face),
+                                        vh);
+  }
+  iv_it = to_face->splice_isolated_vertices(*from_face);
+  while (iv_it != to_face->isolated_vertices_end()) {
+    DVertex* v = &(*iv_it++);
+    Vertex_handle vh(v);
+    _notify_after_move_isolated_vertex(vh);
+  }
+}
+
 //-----------------------------------------------------------------------------
 // Create a new vertex and associate it with the given point.
 //
@@ -4874,16 +4901,7 @@ _remove_edge(DHalfedge* e, bool remove_source, bool remove_target)
     if (oc1->halfedge() == he1)
       oc1->set_halfedge(prev1);
 
-    // Move the isolated vertices inside f2 to f1.
-    DIso_vertex_iter iv_it = f2->isolated_vertices_begin();
-    DIso_vertex_iter iv_to_move;
-    while (iv_it != f2->isolated_vertices_end()) {
-      // We increment the isolated vertices itrator before moving the vertex,
-      // because this operation invalidates the iterator.
-      iv_to_move  = iv_it;
-      ++iv_it;
-      _move_isolated_vertex(f2, f1, &(*iv_to_move));
-    }
+    _move_all_isolated_vertices(f2, f1); // move all iso vertices from f2 to f1
 
     // If he1 or he2 are the incident halfedges to their target vertices,
     // we replace them by the appropriate predecessors.
@@ -4987,17 +5005,7 @@ _remove_edge(DHalfedge* e, bool remove_source, bool remove_target)
     curr->set_inner_ccb(ic1);
 
   _move_all_inner_ccb(f2, f1);          // move the inner CCBs from f2 to f1
-
-  // Move the isolated vertices inside f2 to f1.
-  DIso_vertex_iter iv_it = f2->isolated_vertices_begin();
-  DIso_vertex_iter iv_to_move;
-  while (iv_it != f2->isolated_vertices_end()) {
-    // We increment the isolated vertices itrator before moving the vertex,
-    // because this operation invalidates the iterator.
-    iv_to_move  = iv_it;
-    ++iv_it;
-    _move_isolated_vertex(f2, f1, &(*iv_to_move));
-  }
+  _move_all_isolated_vertices(f2, f1);  // move all iso vertices from f2 to f1
 
   // Notice that f2 will be merged with f1, but its boundary will still be
   // a hole inside this face. In case he1 is a represantative of this hole,
diff --git a/Arrangement_on_surface_2/include/CGAL/Arrangement_on_surface_2.h b/Arrangement_on_surface_2/include/CGAL/Arrangement_on_surface_2.h
index ba7f166611e..8485b0d63ad 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arrangement_on_surface_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arrangement_on_surface_2.h
@@ -1907,6 +1907,13 @@ protected:
    */
   void _move_isolated_vertex(DFace* from_face, DFace* to_face, DVertex* v);
 
+  /*!
+   * Move all isolated vertices from one face to another.
+   * \param from_face The face currently containing the isolated vertices.
+   * \param to_face The face into which we should move the isolated vertices.
+   */
+  void _move_all_isolated_vertices(DFace* from_face, DFace* to_face);
+
   /*!
    * Create a new vertex and associate it with the given point.
    * \param p The point.