diff --git a/STL_Extension/include/CGAL/Hidden_point_memory_policy.h b/STL_Extension/include/CGAL/Hidden_point_memory_policy.h
new file mode 100644
index 00000000000..6552881514e
--- /dev/null
+++ b/STL_Extension/include/CGAL/Hidden_point_memory_policy.h
@@ -0,0 +1,35 @@
+// Copyright (c) 2017  INRIA Sophia-Antipolis (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// Author(s)     : Mael Rouxel-Labbé
+
+#ifndef CGAL_HIDDEN_POINT_MEMORY_POLICY_H
+#define CGAL_HIDDEN_POINT_MEMORY_POLICY_H
+
+#include <CGAL/tags.h>
+
+namespace CGAL {
+
+// A policy to select whether hidden points should be cached in cells or discarded
+// during the construction of a regular triangulation.
+
+template < typename Tag >
+struct Hidden_points_memory_policy : public Tag { };
+
+typedef Hidden_points_memory_policy<Tag_true> Keep_hidden_points;
+typedef Hidden_points_memory_policy<Tag_false> Discard_hidden_points;
+
+} // namespace CGAL
+
+#endif // CGAL_HIDDEN_POINT_MEMORY_POLICY_H
diff --git a/Triangulation_3/include/CGAL/Regular_triangulation_cell_base_3.h b/Triangulation_3/include/CGAL/Regular_triangulation_cell_base_3.h
index 2d19ca3ed46..c69318558ac 100644
--- a/Triangulation_3/include/CGAL/Regular_triangulation_cell_base_3.h
+++ b/Triangulation_3/include/CGAL/Regular_triangulation_cell_base_3.h
@@ -25,20 +25,23 @@
 
 #include <CGAL/license/Triangulation_3.h>
 
+#include <CGAL/Hidden_point_memory_policy.h>
+#include <CGAL/Triangulation_cell_base_3.h>
+
+#include <boost/core/enable_if.hpp>
 
 #include <list>
-#include <CGAL/Triangulation_cell_base_3.h>
 
 namespace CGAL {
 
 template < typename GT,
            typename Cb = Triangulation_cell_base_3<GT >,
+           typename Memory_policy = Keep_hidden_points,
            typename C = std::list<typename GT::Weighted_point_3> >
 class Regular_triangulation_cell_base_3
   : public Cb
 {
 public:
-  static const bool DO_HIDE_POINT = true;
   typedef typename Cb::Vertex_handle                   Vertex_handle;
   typedef typename Cb::Cell_handle                     Cell_handle;
 
@@ -53,8 +56,8 @@ public:
 
   template < typename TDS2 >
   struct Rebind_TDS {
-    typedef typename Cb::template Rebind_TDS<TDS2>::Other     Cb2;
-    typedef Regular_triangulation_cell_base_3<GT, Cb2, C>     Other;
+    typedef typename Cb::template Rebind_TDS<TDS2>::Other                 Cb2;
+    typedef Regular_triangulation_cell_base_3<GT, Cb2, Memory_policy, C>  Other;
   };
 
   Regular_triangulation_cell_base_3()
@@ -76,14 +79,45 @@ public:
                                     Cell_handle   n3)
     : Cb(v0, v1, v2, v3, n0, n1, n2, n3) {}
 
-  Point_iterator hidden_points_begin() { return _hidden.begin(); }
-  Point_iterator hidden_points_end() { return _hidden.end(); }
+  // Memory_policy is Tag_true -------------------------------------------------
+  template<typename Tag = Memory_policy>
+  Point_iterator hidden_points_begin(typename boost::enable_if_c<Tag::value>::type* = NULL)
+  {  return _hidden.begin(); }
+  template<typename Tag = Memory_policy>
+  Point_iterator hidden_points_end(typename boost::enable_if_c<Tag::value>::type* = NULL)
+  { return _hidden.end(); }
 
-  Point_const_iterator hidden_points_begin() const { return _hidden.begin(); }
-  Point_const_iterator hidden_points_end() const { return _hidden.end(); }
+    // const versions
+  template<typename Tag = Memory_policy>
+  Point_const_iterator hidden_points_begin(typename boost::enable_if_c<Tag::value>::type* = NULL) const
+  { return _hidden.begin(); }
+  template<typename Tag = Memory_policy>
+  Point_const_iterator hidden_points_end(typename boost::enable_if_c<Tag::value>::type* = NULL) const
+  { return _hidden.end(); }
 
-  void hide_point (const Weighted_point &p) { _hidden.push_back(p); }
-  //  void unhide_point (Point_iterator i) { _hidden.delete(i); }
+  template<typename Tag = Memory_policy>
+  void hide_point(const Weighted_point& p, typename boost::enable_if_c<Tag::value>::type* = NULL)
+  { _hidden.push_back(p); }
+
+  // Memory_policy is Tag_false ------------------------------------------------
+  template<typename Tag = Memory_policy>
+  Point_iterator hidden_points_begin(typename boost::disable_if_c<Tag::value>::type* = NULL)
+  { return hidden_points_end(); }
+  template<typename Tag = Memory_policy>
+  Point_iterator hidden_points_end(typename boost::disable_if_c<Tag::value>::type* = NULL)
+  { return _hidden.end(); }
+
+    // const versions
+  template<typename Tag = Memory_policy>
+  Point_const_iterator hidden_points_begin(typename boost::disable_if_c<Tag::value>::type* = NULL) const
+  { return hidden_points_end(); }
+  template<typename Tag = Memory_policy>
+  Point_const_iterator hidden_points_end(typename boost::disable_if_c<Tag::value>::type* = NULL) const
+  { return _hidden.end(); }
+
+  template<typename Tag = Memory_policy>
+  void hide_point(const Weighted_point&, typename boost::disable_if_c<Tag::value>::type* = NULL)
+  { }
 
   //note this function is not requested by the RegularTriangulationCellBase_3
   //it should be replaced everywhere by weighted_circumcenter()