diff --git a/Mesh_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h b/Mesh_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h
index 787bf3c7640..c18be2bc370 100644
--- a/Mesh_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h
+++ b/Mesh_3/include/CGAL/IO/Complex_3_in_triangulation_3_to_vtk.h
@@ -15,7 +15,7 @@
 
 #include <CGAL/license/Mesh_3.h>
 
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 
 #include <vtkPoints.h>
 #include <vtkUnstructuredGrid.h>
diff --git a/Mesh_3/include/CGAL/IO/File_maya.h b/Mesh_3/include/CGAL/IO/File_maya.h
index 0eb232d0544..dfb7398d498 100644
--- a/Mesh_3/include/CGAL/IO/File_maya.h
+++ b/Mesh_3/include/CGAL/IO/File_maya.h
@@ -14,7 +14,7 @@
 
 #include <CGAL/license/Mesh_3.h>
 
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 #include <CGAL/utility.h>
 
 #include <boost/unordered_map.hpp>
diff --git a/Mesh_3/include/CGAL/IO/File_tetgen.h b/Mesh_3/include/CGAL/IO/File_tetgen.h
index ef00fad211b..9feaa354ef9 100644
--- a/Mesh_3/include/CGAL/IO/File_tetgen.h
+++ b/Mesh_3/include/CGAL/IO/File_tetgen.h
@@ -15,7 +15,7 @@
 
 #include <CGAL/license/Mesh_3.h>
 
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 #include <CGAL/IO/File_medit.h>
 
 #include <iostream>
diff --git a/Mesh_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h b/Mesh_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
index 718e7baab0c..132df01c693 100644
--- a/Mesh_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
+++ b/Mesh_3/include/CGAL/IO/facets_in_complex_3_to_triangle_mesh.h
@@ -18,9 +18,9 @@
 
 #include <CGAL/array.h>
 #include <CGAL/boost/graph/Euler_operations.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
 #include <CGAL/Polygon_mesh_processing/orient_polygon_soup.h>
 #include <CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h>
+#include <CGAL/Time_stamper.h>
 
 #include <boost/unordered_map.hpp>
 #include <boost/tuple/tuple.hpp>
diff --git a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
index 3f4421ed3e9..a27c9556cb0 100644
--- a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
+++ b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
@@ -26,7 +26,7 @@
 
 #include <CGAL/linear_least_squares_fitting_3.h>
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 #include <CGAL/tuple.h>
 #include <CGAL/iterator.h>
 #include <CGAL/array.h>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Detect_polylines_in_polyhedra.h b/Mesh_3/include/CGAL/Mesh_3/Detect_polylines_in_polyhedra.h
index d71d60c1195..226421ef980 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Detect_polylines_in_polyhedra.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Detect_polylines_in_polyhedra.h
@@ -19,7 +19,7 @@
 #include <CGAL/Compare_handles_with_or_without_timestamps.h>
 #include <CGAL/Mesh_3/Detect_polylines_in_polyhedra_fwd.h>
 #include <CGAL/Default.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 
 #include <boost/mpl/if.hpp>
 #include <boost/unordered_map.hpp>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h b/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
index 1bed83025b7..387f1e9c1f1 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
@@ -23,7 +23,7 @@
 #include <CGAL/Mesh_3/config.h>
 #include <CGAL/Mesh_3/Uniform_sizing_field.h>
 
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 #include <CGAL/convex_hull_2.h>
 #include <CGAL/ch_graham_andrew.h>
 
diff --git a/Mesh_3/include/CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h b/Mesh_3/include/CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h
index e621c87d4b1..b2cd9715ee5 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h
@@ -31,7 +31,7 @@
 #include <CGAL/Bbox_3.h>
 #include <CGAL/Mesh_3/io_signature.h>
 #include <CGAL/Union_find.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 
 #include <boost/functional/hash.hpp>
 #include <boost/unordered_map.hpp>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Mesh_global_optimizer.h b/Mesh_3/include/CGAL/Mesh_3/Mesh_global_optimizer.h
index 0e4145b26f7..cd4310bf5fb 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Mesh_global_optimizer.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Mesh_global_optimizer.h
@@ -29,8 +29,8 @@
 #include <CGAL/Origin.h>
 #include <CGAL/Mesh_optimization_return_code.h>
 #include <CGAL/Mesh_3/Null_global_optimizer_visitor.h>
+#include <CGAL/Time_stamper.h>
 
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
 #include <CGAL/iterator.h>
 #include <CGAL/tuple.h>
 
diff --git a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
index 7516d6e6656..3fdc4cf0b0b 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Protect_edges_sizing_field.h
@@ -41,8 +41,7 @@
 #endif
 
 #include <CGAL/enum.h>
-#include <CGAL/Has_timestamp.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 #include <CGAL/internal/Has_member_visited.h>
 #include <CGAL/iterator.h>
 #include <CGAL/number_utils.h>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Refine_facets_manifold_base.h b/Mesh_3/include/CGAL/Mesh_3/Refine_facets_manifold_base.h
index 8939cbce2a3..1568ea059aa 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Refine_facets_manifold_base.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Refine_facets_manifold_base.h
@@ -19,9 +19,9 @@
 
 #include <CGAL/Mesh_facet_topology.h>
 
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
-#include <CGAL/utility.h>
 #include <CGAL/atomic.h>
+#include <CGAL/utility.h>
+#include <CGAL/Time_stamper.h>
 
 #include <boost/bimap.hpp>
 #include <boost/bimap/unordered_set_of.hpp>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h b/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h
index 9d5a69d4c2b..ac6e886e4a3 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h
@@ -42,8 +42,7 @@
 #include <CGAL/Real_timer.h>
 #include <CGAL/Mesh_3/Null_perturber_visitor.h>
 #include <CGAL/Mesh_3/sliver_criteria.h>
-#include <CGAL/Has_timestamp.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 
 #include <CGAL/Mesh_3/Concurrent_mesher_config.h>
 #include <CGAL/Mesh_3/Worksharing_data_structures.h>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Triangulation_helpers.h b/Mesh_3/include/CGAL/Mesh_3/Triangulation_helpers.h
index 8ac0c8e2340..5eafdc611a1 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Triangulation_helpers.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Triangulation_helpers.h
@@ -21,7 +21,7 @@
 
 #include <CGAL/enum.h>
 #include <CGAL/internal/Has_nested_type_Bare_point.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 
 #include <boost/mpl/if.hpp>
 #include <boost/mpl/identity.hpp>
diff --git a/Mesh_3/include/CGAL/Mesh_3/vertex_perturbation.h b/Mesh_3/include/CGAL/Mesh_3/vertex_perturbation.h
index 82bafa3f43b..07ceaabc6d0 100644
--- a/Mesh_3/include/CGAL/Mesh_3/vertex_perturbation.h
+++ b/Mesh_3/include/CGAL/Mesh_3/vertex_perturbation.h
@@ -24,6 +24,7 @@
 
 #include <CGAL/Mesh_3/C3T3_helpers.h>
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
+#include <CGAL/Time_stamper.h>
 
 #ifdef CGAL_MESH_3_PERTURBER_VERBOSE
   #include <CGAL/Timer.h>
diff --git a/Mesh_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h b/Mesh_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h
index 9ab9148c55f..954478ccee7 100644
--- a/Mesh_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h
+++ b/Mesh_3/include/CGAL/Mesh_complex_3_in_triangulation_3.h
@@ -22,10 +22,10 @@
 
 #include <CGAL/disable_warnings.h>
 #include <CGAL/iterator.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
 #include <CGAL/Mesh_3/utilities.h>
 #include <CGAL/Mesh_3/Mesh_complex_3_in_triangulation_3_base.h>
 #include <CGAL/internal/Mesh_3/Boundary_of_subdomain_of_complex_3_in_triangulation_3_to_off.h>
+#include <CGAL/Time_stamper.h>
 
 #include <boost/bimap/bimap.hpp>
 #include <boost/bimap/multiset_of.hpp>
diff --git a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h
index ad881bb4017..e27c762ed34 100644
--- a/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h
+++ b/Periodic_3_mesh_3/include/CGAL/Periodic_3_mesh_3/Protect_edges_sizing_field.h
@@ -40,13 +40,12 @@
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
 
 #include <CGAL/enum.h>
-#include <CGAL/Has_timestamp.h>
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
 #include <CGAL/internal/Has_member_visited.h>
 #include <CGAL/iterator.h>
 #include <CGAL/number_utils.h>
 #include <CGAL/Periodic_3_Delaunay_triangulation_traits_3.h>
 #include <CGAL/Periodic_3_Delaunay_triangulation_3.h>
+#include <CGAL/Time_stamper.h>
 
 #include <CGAL/boost/iterator/transform_iterator.hpp>
 
diff --git a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
index 9c50a2691c0..acb3b35decd 100644
--- a/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
+++ b/Periodic_3_mesh_3/include/CGAL/refine_periodic_3_mesh_3.h
@@ -24,8 +24,7 @@
 #include <CGAL/Mesh_3/Dump_c3t3.h>
 #include <CGAL/Mesh_3/Triangulation_helpers.h>
 #include <CGAL/refine_mesh_3.h>
-
-#include <CGAL/Hash_handles_with_or_without_timestamps.h>
+#include <CGAL/Time_stamper.h>
 
 #include <boost/parameter/preprocessor.hpp>
 #include <boost/unordered_set.hpp>
diff --git a/STL_Extension/include/CGAL/Hash_handles_with_or_without_timestamps.h b/STL_Extension/include/CGAL/Hash_handles_with_or_without_timestamps.h
deleted file mode 100644
index 1b557a4bca0..00000000000
--- a/STL_Extension/include/CGAL/Hash_handles_with_or_without_timestamps.h
+++ /dev/null
@@ -1,50 +0,0 @@
-// Copyright (c) 2014-2017 GeometryFactory Sarl (France)
-// All rights reserved.
-//
-// This file is part of CGAL (www.cgal.org)
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
-//
-// Author(s)     : Laurent Rineau,
-//                 Mael Rouxel-Labbé
-
-#ifndef CGAL_HASH_HANDLES_WITH_OR_WITHOUT_TIMESTAMPS_H
-#define CGAL_HASH_HANDLES_WITH_OR_WITHOUT_TIMESTAMPS_H
-
-#include <CGAL/Has_timestamp.h>
-
-#include <boost/functional/hash.hpp>
-
-#include <cstddef>
-#include <iterator>
-
-namespace CGAL {
-
-struct Hash_handles_with_or_without_timestamps
-{
-  template <typename Handle>
-  std::size_t operator()(const Handle h) const
-  {
-    typedef typename std::iterator_traits<Handle>::value_type Type;
-
-    return hash(h, Boolean_tag<CGAL::internal::Has_timestamp<Type>::value>());
-  }
-
-  template<typename Handle>
-  std::size_t hash(const Handle h, Tag_false) const
-  {
-    return boost::hash_value(&*h);
-  }
-
-  template<typename Handle>
-  std::size_t hash(const Handle h, Tag_true) const
-  {
-    return h->time_stamp();
-  }
-};
-
-} // namespace CGAL
-
-#endif // CGAL_HASH_HANDLES_WITH_OR_WITHOUT_TIMESTAMPS_H
diff --git a/STL_Extension/include/CGAL/Time_stamper.h b/STL_Extension/include/CGAL/Time_stamper.h
index 82961b37269..7385f4473eb 100644
--- a/STL_Extension/include/CGAL/Time_stamper.h
+++ b/STL_Extension/include/CGAL/Time_stamper.h
@@ -149,6 +149,17 @@ struct Get_time_stamper<T,false>{
 template <class T>
 struct Time_stamper_impl : public Get_time_stamper<T>::type {};
 
+struct Hash_handles_with_or_without_timestamps
+{
+  template <typename Handle>
+  std::size_t operator()(const Handle h) const
+  {
+    typedef typename std::iterator_traits<Handle>::value_type Type;
+
+    return Get_time_stamper<Type>::type::hash_value(&*h);
+  }
+};
+
 } //end of namespace CGAL
 
 #endif // CGAL_TIME_STAMPER_H