diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_euclidean_traits_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_euclidean_traits_2.h
deleted file mode 100644
index 528669bf2af..00000000000
--- a/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_euclidean_traits_2.h
+++ /dev/null
@@ -1,25 +0,0 @@
-
-namespace CGAL {
-
-/*!
-\ingroup PkgTriangulation2TraitsClasses
-
-\deprecated The class is deprecated since \cgal 4.10, as the weighted point and the function
-objects for weighted points are part of the concept `Kernel`. The class is kept for backward
-compatibility, but ignores the template parameter `Weight`.
-
-\tparam K must be a model of the `Kernel` concept.
-
-\tparam Weight This template parameter is ignored, as `Kernel::Weighted_point_2`
-               uses the type `Kernel::FT`.
-
-\cgalModels `RegularTriangulationTraits_2`
-
-*/
-template< typename K, typename Weight >
-class Regular_triangulation_euclidean_traits_2 : public K {
-public:
-
-}; /* end Regular_triangulation_euclidean_traits_2 */
-
-} /* end namespace CGAL */
diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_filtered_traits_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_filtered_traits_2.h
deleted file mode 100644
index 966360717cd..00000000000
--- a/Triangulation_2/doc/Triangulation_2/CGAL/Regular_triangulation_filtered_traits_2.h
+++ /dev/null
@@ -1,18 +0,0 @@
-
-namespace CGAL {
-
-/*!
-\ingroup PkgTriangulation2TraitsClasses
-
-\deprecated This class is deprecated, as the predicates and constructions that operate
-on weighted points are now define in the concept `Kernel`, and are dealt with by filtered kernels.
-
-*/
-template< typename FK >
-class Regular_triangulation_filtered_traits_2 {
-public:
-
-/// @}
-
-}; /* end Regular_triangulation_filtered_traits_2 */
-} /* end namespace CGAL */
diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Triangulation_euclidean_traits_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Triangulation_euclidean_traits_2.h
deleted file mode 100644
index 3dcf5fbe4e7..00000000000
--- a/Triangulation_2/doc/Triangulation_2/CGAL/Triangulation_euclidean_traits_2.h
+++ /dev/null
@@ -1,36 +0,0 @@
-
-namespace CGAL {
-
-/*!
-\ingroup PkgTriangulation2TraitsClasses
-
-\deprecated This class is deprecated since \cgal 4.9.  Instead of using it, pass directly the kernel.
-
-
-The class `Triangulation_euclidean_traits_2` can be used to instantiate the geometric traits 
-class of basic and Delaunay triangulations. 
-The template parameter `K` has to 
-be instantiated by a model of the `Kernel` concept. 
-The class `Triangulation_euclidean_traits_2` uses types 
-and predicates defined in `K`. 
-
-\cgalModels `TriangulationTraits_2`
-\cgalModels `DelaunayTriangulationTraits_2`
-
-\sa `TriangulationTraits_2` 
-\sa `DelaunayTriangulationTraits_2` 
-\sa `CGAL::Triangulation_2<Traits,Tds>` 
-\sa `CGAL::Delaunay_triangulation_2<Traits,Tds>` 
-\sa `CGAL::Projection_traits_xy_3<K>`
-\sa `CGAL::Projection_traits_xz_3<K>`
-\sa `CGAL::Projection_traits_yz_3<K>`
-
-*/
-template< typename K >
-class Triangulation_euclidean_traits_2 {
-public:
-
-/// @}
-
-}; /* end Triangulation_euclidean_traits_2 */
-} /* end namespace CGAL */
diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Weighted_point.h b/Triangulation_2/doc/Triangulation_2/CGAL/Weighted_point.h
deleted file mode 100644
index 4ba396a63ff..00000000000
--- a/Triangulation_2/doc/Triangulation_2/CGAL/Weighted_point.h
+++ /dev/null
@@ -1,83 +0,0 @@
-
-namespace CGAL {
-
-/*!
-\ingroup PkgTriangulation2Miscellaneous
-
-\deprecated This class is deprecated, as 2D and 3D weighted point classes are now part of the concept `Kernel`.
-
-
-The class `Weighted_point` provides a type associating 
-a point type `Pt` with a weight type `Wt`. 
-It was used in the traits classes `Regular_triangulation_euclidean_traits_2`
-and `Regular_triangulation_euclidean_traits_3`, which are now also deprecated.
-
-\sa `CGAL::Regular_triangulation_euclidean_traits_2<Rep,Weight>` 
-\sa `CGAL::Regular_triangulation_euclidean_traits_3<R,Weight>`
-
-*/
-template< typename Pt, typename Wt >
-class Weighted_point : public Pt {
-public:
-
-/// \name Types 
-/// @{
-
-/*!
-The point type 
-*/ 
-Pt Point; 
-
-/*!
-The weight type. 
-*/ 
-Wt Weight; 
-
-/// @} 
-
-/// \name Creation 
-/// @{
-
-/*!
-copy constructor. 
-*/ 
-Weighted_point(Weighted_point wq); 
-
-/*!
-
-*/ 
-Weighted_point(Point p=Point(), Weight w= Weight(0)); 
-
-/*!
-Constructs the point from `x` 
-and `y` coordinates, with a weight of 0. Requires that the ambient 
-dimension be 2. 
-*/ 
-Weighted_point(FT x, FT y); 
-
-/*!
-Constructs the point from 
-`x`, `y` and `z` coordinates, with a weight of 0. Requires that 
-the ambient dimension be 3. 
-*/ 
-Weighted_point(FT x, FT y, FT z); 
-
-/// @} 
-
-/// \name Access Functions 
-/// @{
-
-/*!
-
-*/ 
-Point point() const; 
-
-/*!
-
-*/ 
-Weight weight() const; 
-
-/// @}
-
-}; /* end Weighted_point */
-} /* end namespace CGAL */
diff --git a/Triangulation_2/doc/Triangulation_2/PackageDescription.txt b/Triangulation_2/doc/Triangulation_2/PackageDescription.txt
index a4693d82031..d199da9f5a3 100644
--- a/Triangulation_2/doc/Triangulation_2/PackageDescription.txt
+++ b/Triangulation_2/doc/Triangulation_2/PackageDescription.txt
@@ -6,9 +6,6 @@
 /// \ingroup PkgTriangulation2Ref
 
 
-/// \defgroup PkgTriangulation2TraitsClasses Traits Classes
-/// \ingroup PkgTriangulation2Ref
-
 /// \defgroup PkgTriangulation2VertexFaceClasses Vertex and Face Classes
 /// \ingroup PkgTriangulation2Ref
 
@@ -95,9 +92,6 @@ are described in Chapter \ref PkgTDS2Ref "2D Triangulation Data Structure".
 - `CGAL::Constrained_triangulation_plus_2<Tr>`
 - `CGAL::Triangulation_hierarchy_2<Tr>`
 
-- `CGAL::Regular_triangulation_euclidean_traits_2<K,Weight>`
-- `CGAL::Regular_triangulation_filtered_traits_2<FK>`
-
 - `CGAL::Triangulation_face_base_2<Traits,Fb>`
 - `CGAL::Triangulation_vertex_base_2<Traits,Vb>`
 - `CGAL::Regular_triangulation_face_base_2<Traits,Fb>`
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h
index 02acad6d80a..8f73fc9dd9a 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h
@@ -28,7 +28,7 @@
 
 #include <CGAL/triangulation_assertions.h>
 #include <CGAL/Polygon_2.h>
-#include <CGAL/Polyline_constraint_hierarchy_2.h>
+#include <CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h>
 #include <boost/tuple/tuple.hpp>
 
 #include <CGAL/Default.h>
diff --git a/Triangulation_2/include/CGAL/Distance_2.h b/Triangulation_2/include/CGAL/Distance_2.h
deleted file mode 100644
index 8b5f1325971..00000000000
--- a/Triangulation_2/include/CGAL/Distance_2.h
+++ /dev/null
@@ -1,106 +0,0 @@
-// Copyright (c) 1997  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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-// 
-//
-// Author(s)     : Mariette Yvinec
-//                 Sylvain Pion
-
-#ifndef CGAL_DISTANCE_2_H
-#define CGAL_DISTANCE_2_H
-
-#include <CGAL/license/Triangulation_2.h>
-
-
-#include <CGAL/assertions.h>
-#include <CGAL/distance_predicates_2.h>
-
-namespace CGAL {
-
-template <class I>
-struct Distance_2
-{
-  typedef typename I::Point Point;
-
-  Distance_2(const I* = NULL) {}
-
-  Distance_2(const Point& p0, const I* = NULL)
-  { p[0]=p0; }
-
-  Distance_2(const Point& p0, const Point& p1, const I* = NULL)
-  { p[0]=p0; p[1]=p1; }
-
-  Distance_2(const Point& p0, const Point& p1, const Point& p2, 
-	     const I* = NULL)
-  { p[0]=p0; p[1]=p1; p[2]=p2; }
-
-  void set_point(int i, const Point& q)
-  {
-    CGAL_precondition( ((unsigned int) i) < 3 );
-    p[i] = q;
-  }
-
-  Point get_point(int i) const
-  {
-    CGAL_precondition( ((unsigned int) i) < 3 );
-    return p[i];
-  }
-
-  Comparison_result compare() const
-  {
-    return cmp_dist_to_point(p[0], p[1], p[2]);
-  }
-
-private:
-  Point p[3];
-};
-
-template <class Traits>
-struct Distance_xy_3  : public Distance_2<Traits> 
-{
-  typedef typename Distance_2<Traits>::Point Point;
-
-public:
-  Distance_xy_3(const Point& p0,
-	   const Traits* traits = NULL)
-    : Distance_2<Traits>(p0, traits) { }
-    
-    
-  Distance_xy_3(const Point& p0,
-	   const Point& p1,
-	   const Traits* traits = NULL)
-    : Distance_2<Traits>(p0,p1,traits) { }
-    
-  Distance_xy_3(const Point& p0,
-	   const Point& p1,
-	   const Point& p2,
-	   const Traits* traits = NULL)
-    : Distance_2<Traits>(p0,p1,p2,traits) { }
-    
-  Comparison_result
-  compare() const
-    {
-      Point p0 = this->get_point(0);
-      Point p1 = this->get_point(1);
-      Point p2 = this->get_point(2);
-      return cmp_dist_to_pointC2(x(p0),y(p0),x(p1),y(p1),x(p2),y(p2));
-    }
-};
-
-} //namespace CGAL
-
-#endif // CGAL_DISTANCE_2_H
diff --git a/Triangulation_2/include/CGAL/Regular_triangulation_euclidean_traits_2.h b/Triangulation_2/include/CGAL/Regular_triangulation_euclidean_traits_2.h
deleted file mode 100644
index 7d1751d55e6..00000000000
--- a/Triangulation_2/include/CGAL/Regular_triangulation_euclidean_traits_2.h
+++ /dev/null
@@ -1,46 +0,0 @@
-// Copyright (c) 1997   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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-//
-// Author(s)     : Mariette Yvinec <Mariette.Yvinec@sophia.inria.fr>
-//                 Sylvain Pion
-
-#ifndef CGAL_REGULAR_TRIANGULATION_EUCLIDEAN_TRAITS_2_H
-#define CGAL_REGULAR_TRIANGULATION_EUCLIDEAN_TRAITS_2_H
-
-#include <CGAL/license/Triangulation_2.h>
-
-#define CGAL_DEPRECATED_HEADER "<CGAL/Regular_triangulation_euclidean_traits_2.h>"
-#define CGAL_DEPRECATED_MESSAGE_DETAILS \
-  "The kernel K can be used directly as traits since weighted points and "\
-  "the associated function objects are now part of the concept Kernel."
-#include <CGAL/internal/deprecation_warning.h>
-
-namespace CGAL {
-
-template < class K, class W = typename K::RT>
-class Regular_triangulation_euclidean_traits_2
-  : public K
-{
-public:
-  Regular_triangulation_euclidean_traits_2() {}
-  Regular_triangulation_euclidean_traits_2(const K& k) : K(k) {}
-};
-
-} //namespace CGAL
-
-#endif // CGAL_REGULAR_TRIANGULATION_EUCLIDEAN_TRAITS_2_H
diff --git a/Triangulation_2/include/CGAL/Regular_triangulation_filtered_traits_2.h b/Triangulation_2/include/CGAL/Regular_triangulation_filtered_traits_2.h
deleted file mode 100644
index 90f63a9e77e..00000000000
--- a/Triangulation_2/include/CGAL/Regular_triangulation_filtered_traits_2.h
+++ /dev/null
@@ -1,22 +0,0 @@
-// Copyright (c) 2004   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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-// 
-//
-// Author(s)     : Sylvain Pion
-
-// kept for backward compatibility
diff --git a/Triangulation_2/include/CGAL/Triangulation_2.h b/Triangulation_2/include/CGAL/Triangulation_2.h
index 16e355c20e4..eba46c6699b 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2.h
@@ -41,7 +41,7 @@
 #include <CGAL/Triangulation_data_structure_2.h>
 #include <CGAL/Triangulation_vertex_base_2.h>
 #include <CGAL/Triangulation_face_base_2.h>
-#include <CGAL/Triangulation_line_face_circulator_2.h>
+#include <CGAL/Triangulation_2/internal/Triangulation_line_face_circulator_2.h>
 #include <CGAL/spatial_sort.h>
 #include <CGAL/Spatial_sort_traits_adapter_2.h>
 
diff --git a/Triangulation_2/include/CGAL/Constraint_hierarchy_2.h b/Triangulation_2/include/CGAL/Triangulation_2/internal/Constraint_hierarchy_2.h
similarity index 100%
rename from Triangulation_2/include/CGAL/Constraint_hierarchy_2.h
rename to Triangulation_2/include/CGAL/Triangulation_2/internal/Constraint_hierarchy_2.h
diff --git a/Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h b/Triangulation_2/include/CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h
similarity index 100%
rename from Triangulation_2/include/CGAL/Polyline_constraint_hierarchy_2.h
rename to Triangulation_2/include/CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h
diff --git a/Triangulation_2/include/CGAL/internal/Triangulation_2_filtered_projection_traits_3.h b/Triangulation_2/include/CGAL/Triangulation_2/internal/Triangulation_2_filtered_projection_traits_3.h
similarity index 97%
rename from Triangulation_2/include/CGAL/internal/Triangulation_2_filtered_projection_traits_3.h
rename to Triangulation_2/include/CGAL/Triangulation_2/internal/Triangulation_2_filtered_projection_traits_3.h
index 07fc6bba994..4d06dda4b85 100644
--- a/Triangulation_2/include/CGAL/internal/Triangulation_2_filtered_projection_traits_3.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2/internal/Triangulation_2_filtered_projection_traits_3.h
@@ -26,7 +26,7 @@
 #include <CGAL/license/Triangulation_2.h>
 
 
-#include <CGAL/internal/Triangulation_2_projection_traits_base_3.h>
+#include <CGAL/Triangulation_2/internal/Triangulation_2_projection_traits_base_3.h>
 #include <CGAL/Filtered_predicate_with_state.h>
 
 namespace CGAL {
diff --git a/Triangulation_2/include/CGAL/internal/Triangulation_2_projection_traits_base_3.h b/Triangulation_2/include/CGAL/Triangulation_2/internal/Triangulation_2_projection_traits_base_3.h
similarity index 100%
rename from Triangulation_2/include/CGAL/internal/Triangulation_2_projection_traits_base_3.h
rename to Triangulation_2/include/CGAL/Triangulation_2/internal/Triangulation_2_projection_traits_base_3.h
diff --git a/Triangulation_2/include/CGAL/Triangulation_line_face_circulator_2.h b/Triangulation_2/include/CGAL/Triangulation_2/internal/Triangulation_line_face_circulator_2.h
similarity index 100%
rename from Triangulation_2/include/CGAL/Triangulation_line_face_circulator_2.h
rename to Triangulation_2/include/CGAL/Triangulation_2/internal/Triangulation_line_face_circulator_2.h
diff --git a/Triangulation_2/include/CGAL/Triangulation_2_filtered_projection_traits_3.h b/Triangulation_2/include/CGAL/Triangulation_2_filtered_projection_traits_3.h
deleted file mode 100644
index f0e428d7620..00000000000
--- a/Triangulation_2/include/CGAL/Triangulation_2_filtered_projection_traits_3.h
+++ /dev/null
@@ -1,34 +0,0 @@
- // Copyright (c) 2009  GeometryFactory (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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-// 
-//
-// Author(s)     : Laurent Rineau
-
-
-#ifndef CGAL_TRIANGULATION_2_FILTERED_PROJECTION_TRAITS_3_H
-#define CGAL_TRIANGULATION_2_FILTERED_PROJECTION_TRAITS_3_H
-
-#include <CGAL/license/Triangulation_2.h>
-
-#define CGAL_DEPRECATED_HEADER "<CGAL/Triangulation_2_filtered_projection_traits_3.h>"
-#define CGAL_REPLACEMENT_HEADER "<CGAL/Triangulation_2_projection_traits_3.h>"
-#include <CGAL/internal/deprecation_warning.h>
-
-#include <CGAL/Triangulation_2_projection_traits_3.h>
-
-#endif // CGAL_TRIANGULATION_2_FILTERED_PROJECTION_TRAITS_3_H
diff --git a/Triangulation_2/include/CGAL/Triangulation_2_projection_traits_3.h b/Triangulation_2/include/CGAL/Triangulation_2_projection_traits_3.h
index 66a0bae5e70..b0eb7b71efb 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2_projection_traits_3.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2_projection_traits_3.h
@@ -26,7 +26,7 @@
 #include <CGAL/license/Triangulation_2.h>
 
 
-#include <CGAL/internal/Triangulation_2_filtered_projection_traits_3.h>
+#include <CGAL/Triangulation_2/internal/Triangulation_2_filtered_projection_traits_3.h>
 
 namespace CGAL{
 
diff --git a/Triangulation_2/include/CGAL/Triangulation_euclidean_traits_2.h b/Triangulation_2/include/CGAL/Triangulation_euclidean_traits_2.h
deleted file mode 100644
index 70e81bd11f0..00000000000
--- a/Triangulation_2/include/CGAL/Triangulation_euclidean_traits_2.h
+++ /dev/null
@@ -1,140 +0,0 @@
-// Copyright (c) 1997   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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-// 
-//
-// Author(s)     : Mariette Yvinec
-
-#ifndef CGAL_TRIANGULATION_EUCLIDEAN_TRAITS_2_H
-#define CGAL_TRIANGULATION_EUCLIDEAN_TRAITS_2_H
-
-#include <CGAL/license/Triangulation_2.h>
-
-
-#define CGAL_DEPRECATED_HEADER "<CGAL/Triangulation_euclidean_traits_2.h>"
-#include <CGAL/internal/deprecation_warning.h>
-
-#include <CGAL/Point_2.h>
-#include <CGAL/Segment_2.h>
-#include <CGAL/Triangle_2.h>
-#include <CGAL/Line_2.h>
-#include <CGAL/Ray_2.h>
-#include <CGAL/predicates_on_points_2.h>
-#include <CGAL/basic_constructions_2.h>
-#include <CGAL/distance_predicates_2.h>
-
-#include <CGAL/triangulation_assertions.h>
-#include <CGAL/Intersections_2/Segment_2_Segment_2.h>
-
-namespace CGAL { 
-
-template < class R >
-class Triangulation_euclidean_traits_2 {
-public:
-  typedef R Rep;
-  typedef typename R::Point_2     Point_2;
-  typedef typename R::Segment_2   Segment_2;
-  typedef typename R::Triangle_2  Triangle_2;
-  typedef typename R::Line_2      Line_2;
-  typedef typename R::Ray_2       Ray_2;
-
-  typedef typename R::Less_x_2                   Less_x_2;
-  typedef typename R::Less_y_2                   Less_y_2;
-  typedef typename R::Compare_x_2                Compare_x_2;
-  typedef typename R::Compare_y_2                Compare_y_2;
-  typedef typename R::Orientation_2              Orientation_2;
-  typedef typename R::Side_of_oriented_circle_2  Side_of_oriented_circle_2;
-  typedef typename R::Construct_circumcenter_2   Construct_circumcenter_2;
-  typedef typename R::Construct_bisector_2       Construct_bisector_2;
-  typedef typename R::Compare_distance_2         Compare_distance_2;
-  typedef typename R::Construct_segment_2        Construct_segment_2;
-  typedef typename R::Construct_triangle_2       Construct_triangle_2;
-  typedef typename R::Construct_direction_2      Construct_direction_2;
-  typedef typename R::Construct_ray_2            Construct_ray_2;
-  
-  //for natural_neighbor_coordinates_2
-  typedef typename R::FT                         FT;
-  typedef typename R::Equal_x_2                  Equal_x_2;
-  typedef typename R::Compute_area_2             Compute_area_2;
-  Compute_area_2 compute_area_2_object () const {return Compute_area_2();}
-  
-  // for compatibility with previous versions
-  typedef Point_2      Point;
-  typedef Segment_2    Segment;
-  typedef Triangle_2   Triangle;
-  typedef Ray_2        Ray;
-  typedef Line_2       Line;
-
-  Triangulation_euclidean_traits_2() {}
-  Triangulation_euclidean_traits_2(const Triangulation_euclidean_traits_2 &) {}
-  Triangulation_euclidean_traits_2 &operator=
-      (const Triangulation_euclidean_traits_2 &)
-  {return *this;}
- 
-  Less_x_2
-  less_x_2_object() const
-    { return Less_x_2();}
-
-  Less_y_2
-  less_y_2_object() const
-    { return Less_y_2();}
-  
-  Compare_x_2
-  compare_x_2_object() const
-    { return Compare_x_2();}
-
-  Compare_y_2
-  compare_y_2_object() const
-    { return Compare_y_2();}
-  
-  Orientation_2
-  orientation_2_object() const
-    { return Orientation_2();}
-
-  Side_of_oriented_circle_2
-  side_of_oriented_circle_2_object() const
-    {return Side_of_oriented_circle_2();}
- 
-  Construct_circumcenter_2
-  construct_circumcenter_2_object() const
-    { return Construct_circumcenter_2();}
-
-  Construct_bisector_2
-  construct_bisector_2_object() const
-    {return Construct_bisector_2();}
-  
-  Compare_distance_2
-  compare_distance_2_object() const
-    {return Compare_distance_2();}
-
-  Construct_segment_2  construct_segment_2_object() const
-    {return Construct_segment_2();}
-
-  Construct_triangle_2  construct_triangle_2_object() const
-    {return Construct_triangle_2();}
-
-  Construct_direction_2  construct_direction_2_object() const
-    {return Construct_direction_2();}
-
-  Construct_ray_2  construct_ray_2_object() const
-    {return Construct_ray_2();}
-
-};
-
-} //namespace CGAL 
-
-#endif // CGAL_TRIANGULATION_EUCLIDEAN_TRAITS_2_H
diff --git a/Triangulation_2/include/CGAL/Triangulation_iterator_adaptator.h b/Triangulation_2/include/CGAL/Triangulation_iterator_adaptator.h
deleted file mode 100644
index 81daa5e3daa..00000000000
--- a/Triangulation_2/include/CGAL/Triangulation_iterator_adaptator.h
+++ /dev/null
@@ -1,60 +0,0 @@
-// Copyright (c) 1997  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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-// 
-//
-// Author(s)     : Mariette Yvinec
-//                 Menelaos Karavelas <mkaravel@cse.nd.edu>
-
-#ifndef CGAL_TRIANGULATION_ITERATOR_ADAPTATOR_H
-#define CGAL_TRIANGULATION_ITERATOR_ADAPTATOR_H
-
-#include <CGAL/license/Triangulation_2.h>
-
-
-#include <CGAL/triangulation_assertions.h>
-
-namespace CGAL {
-
-template <class Base, class Handle>
-struct Triangulation_iterator_handle_adaptor
-  : public Base
-{
-  typedef Triangulation_iterator_handle_adaptor<Base, Handle>  Self;
-  Triangulation_iterator_handle_adaptor() : Base() {}
-   
-  Triangulation_iterator_handle_adaptor(const Base & b) 
-    : Base(b) {}
-
-  // MK: added this to satisfy the mips_CC-7.40 compiler
-  Self& operator=(const Self& other) {
-    static_cast<Base &>(*this) = static_cast<const Base&>(other); 
-    return *this;
-  }
-
-  operator Handle() const {return Base::base();}
-  Self&  operator++() { Base::operator++(); return *this;}
-  Self&  operator--() { Base::operator--(); return *this;}
-  Self   operator++(int) { Self tmp(*this); ++(*this); return tmp; }
-  Self   operator--(int) { Self tmp(*this); --(*this); return tmp; }
-};
-
-
-
-} //namespace CGAL
-
-#endif //CGAL_TRIANGULATION_ITERATOR_ADAPTATOR_H
diff --git a/Triangulation_2/include/CGAL/Trivial_iterator.h b/Triangulation_2/include/CGAL/Trivial_iterator.h
deleted file mode 100644
index a079e8a55ef..00000000000
--- a/Triangulation_2/include/CGAL/Trivial_iterator.h
+++ /dev/null
@@ -1,142 +0,0 @@
-// Copyright (c) 2002  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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-// 
-//
-// Author(s)     : Sylvain Pion
-
-#ifndef CGAL_TRIVIAL_ITERATOR_H
-#define CGAL_TRIVIAL_ITERATOR_H
-
-#include <CGAL/license/Triangulation_2.h>
-
-
-#include <iterator>
-#include <CGAL/iterator.h>
-
-namespace CGAL { 
-
-// TODO :
-// - comparison operators should be global, but it causes problems...
-// - Have a look at Boost's concept_checking and archetypes :
-//   https://www.boost.org/libs/concept_check/concept_check.htm
-
-class Trivial_iterator_tag{};
-
-
-template <class I>
-class Trivial_iterator
-{
-public:
-  typedef I                                                 Iterator;
-  typedef Trivial_iterator<I>                               Self;
-  typedef typename std::iterator_traits<I>::value_type      value_type;
-  typedef typename std::iterator_traits<I>::difference_type difference_type;
-  typedef typename std::iterator_traits<I>::reference       reference;
-  typedef typename std::iterator_traits<I>::pointer         pointer;
-  typedef Trivial_iterator_tag                              iterator_category;
-  // Special for circulators.
-  typedef I_Circulator_size_traits<iterator_category,I>     C_S_Traits;
-  typedef typename  C_S_Traits::size_type                   size_type;
-
-
-  Trivial_iterator() {}
-  Trivial_iterator(const I &i) : base_(i) {}
-
-  // To allow conversion from iterator to const_iterator.
-  template <class Iter>
-  Trivial_iterator(const Trivial_iterator<Iter> &t)
-    : base_(t.base()) {}
-
-  reference operator*() const { return *base_;  }
-  pointer operator->() const  { return &*base_; }
-
-  bool operator==(const Trivial_iterator &b) const { return base()==b.base(); }
-  bool operator!=(const Trivial_iterator &b) const { return base()!=b.base(); }
-
-private:
-  const Iterator & base() const { return base_; }
-
-  Iterator base_;
-};
-
-
-
-class Trivial_comparable_iterator_tag{};
-
-template <class I>
-class Trivial_comparable_iterator
-{
-public:
-  typedef I                                            Iterator;
-  typedef Trivial_comparable_iterator<I>               Self;
-  typedef typename std::iterator_traits<I>::value_type value_type;
-  typedef typename std::iterator_traits<I>::difference_type
-                                                       difference_type;
-  typedef typename std::iterator_traits<I>::reference  reference;
-  typedef typename std::iterator_traits<I>::pointer    pointer;
-  typedef Trivial_comparable_iterator_tag              iterator_category;
-  // Special for circulators.
-  typedef I_Circulator_size_traits<iterator_category,I> C_S_Traits;
-  typedef typename  C_S_Traits::size_type               size_type;
-
-
-  Trivial_comparable_iterator() {}
-  Trivial_comparable_iterator(const I &i) : base_(i) {}
-
-  // To allow conversion from iterator to const_iterator.
-  template <class Iter>
-  Trivial_comparable_iterator(const Trivial_comparable_iterator<Iter> &t)
-    : base_(t.base()) {}
-
-  reference operator*() const { return *base_;  }
-  pointer operator->() const  { return &*base_; }
-
-  bool operator==(const Trivial_comparable_iterator &b) const 
-    { return base()==b.base(); }
-  bool operator!=(const Trivial_comparable_iterator &b) const  
-    { return base()!=b.base(); }
-
-  bool operator< (const Trivial_comparable_iterator &b) const  
-    { return base()< b.base(); }
-  bool operator> (const Trivial_comparable_iterator &b) const  
-    { return base()> b.base(); }
-  bool operator<=(const Trivial_comparable_iterator &b) const  
-    { return base()<=b.base(); }
-  bool operator>=(const Trivial_comparable_iterator &b) const  
-    { return base()>=b.base(); }
-
-private:
-  const Iterator & base() const { return base_; }
-
-  Iterator base_;
-};
-
-
-// Some macros depending on CGAL_NO_CONCEPT_CHECKING.
-#ifndef CGAL_NO_CONCEPT_CHECKING
-#  define CGAL_TRIVIAL_ITERATOR_CHECKER(X)    CGAL::Trivial_iterator<X>
-#  define CGAL_TRIVIAL_COMPARABLE_ITERATOR_CHECKER(X) \
-     CGAL::Trivial_comparable_iterator<X>
-#else
-#  define CGAL_TRIVIAL_ITERATOR_CHECKER(X)    X
-#  define CGAL_TRIVIAL_COMPARABLE_ITERATOR_CHECKER(X) X
-#endif
-
-} //namespace CGAL
-
-#endif // CGAL_TRIVIAL_ITERATOR_H
diff --git a/Triangulation_2/include/CGAL/Weighted_point.h b/Triangulation_2/include/CGAL/Weighted_point.h
deleted file mode 100644
index e208adb2fd4..00000000000
--- a/Triangulation_2/include/CGAL/Weighted_point.h
+++ /dev/null
@@ -1,154 +0,0 @@
-// Copyright (c) 1999-2004  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
-// 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.
-//
-// $URL$
-// $Id$
-// SPDX-License-Identifier: GPL-3.0+
-// 
-//
-// Author(s)     : Mariette Yvinec
-//                 Sylvain Pion
-
-#ifndef CGAL_WEIGHTED_POINT_H
-#define CGAL_WEIGHTED_POINT_H
-
-#include <CGAL/license/Triangulation_2.h>
-
-#define CGAL_DEPRECATED_HEADER "<CGAL/Weighted_point.h>"
-#define CGAL_DEPRECATED_MESSAGE_DETAILS \
-   "Weighted points are now part of the concept Kernel. One should therefore "\
-   "use `CGAL::Weighted_point_2<K>` and `CGAL::Weighted_point_3<K>`."
-#include <CGAL/internal/deprecation_warning.h>
-
-#include <CGAL/Kernel_traits.h>
-#include <CGAL/Dimension.h>
-#include <CGAL/IO/io.h>
-#include <iostream>
-#include <boost/utility/enable_if.hpp>
-#include <boost/type_traits/is_convertible.hpp>
-#include <boost/mpl/and.hpp>
-#include <boost/mpl/bool.hpp>
-#include <boost/mpl/logical.hpp>
-
-namespace CGAL {
-
-template < class Pt, class We >
-class Weighted_point : public Pt
-{
-  typedef typename Kernel_traits<Pt>::Kernel::FT FT;
-public:
-  typedef We Weight;
-  typedef Pt Point;
-
-  Weighted_point ()
-      : Point(), _weight(0) {}
-
-  //explicit
-  Weighted_point (const Point &p)
-      : Point(p), _weight(0)
-  {
-    // CGAL_error_msg( "Warning : truncated weight !!!");
-  }
-
-  Weighted_point (const Point &p, const Weight &w)
-      : Point(p), _weight(w) {}
-
-
-  // Constructors from coordinates are also provided for convenience, except
-  // that they are only from Cartesian coordinates, and with no weight, so as
-  // to avoid any potential ambiguity between the homogeneous weight and the
-  // power weight (it should be easy enough to pass a Point explicitly in those
-  // cases).
-  // The enable_if complexity comes from the fact that we separate dimension 2 and 3.
-
-  template < typename Tx, typename Ty >
-  Weighted_point (const Tx &x, const Ty &y,
-	          typename boost::enable_if< boost::mpl::and_<boost::is_convertible<Tx, FT>,
-					                      boost::is_convertible<Ty, FT>,
-							      boost::mpl::bool_<CGAL::Ambient_dimension<Point>::value == 2> > >::type* = 0)
-      : Point(x, y), _weight(0) {}
-
-  template < typename Tx, typename Ty, typename Tz >
-  Weighted_point (const Tx &x, const Ty &y, const Tz &z,
-	          typename boost::enable_if< boost::mpl::and_<boost::is_convertible<Tx, FT>,
-					                      boost::is_convertible<Ty, FT>,
-					                      boost::is_convertible<Tz, FT>,
-							      boost::mpl::bool_<CGAL::Ambient_dimension<Point>::value == 3> > >::type* = 0)
-      : Point(x, y, z), _weight(0) {}
-
-  const Point & point() const
-  {
-      return *this;
-  }
-
-  const Weight & weight() const
-  {
-      return _weight;
-  }
-
-// The following power() member functions are not used at the moment.
-// They belong to the traits class anyway.
-//
-//  Weight power(const Point &p)
-//  {	
-//      return squared_distance(*this, p) - weight();
-//  }
-// 
-//  Weight power(const Weighted_point &p)
-//  {	
-//      return squared_distance(*this, p) - weight() - p.weight();
-//  }
-
-private:
-  Weight _weight;
-};
-
-
-template < class Point, class Weight >
-std::ostream &
-operator<<(std::ostream &os, const Weighted_point<Point,Weight> &p)
-{
-  switch(get_mode(os))
-  {
-  case IO::ASCII :
-    return os << p.point() <<  " " << p.weight();
-  case IO::BINARY :
-    os << p.point();
-    write(os, p.weight());
-    return os;
-  default:
-    return os << "Weighted_point(" << p.point() << ", " << p.weight() << ")";
-  }
-}
-
-template < class Point, class Weight >
-std::istream &
-operator>>(std::istream &is, Weighted_point<Point,Weight> &wp)
-{
-  Weight w;
-  Point p;
-  is >> p;
-  if(!is) return is;
-  if(is_ascii(is))
-    is >> w;
-  else
-    read(is, w);
-  if (is)
-    wp = Weighted_point<Point,Weight>(p,w);
-  return is;
-}
-
-} // namespace CGAL
-
-#endif // CGAL_WEIGHTED_POINT_H
diff --git a/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_hierarchy_2.h b/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_hierarchy_2.h
index cc4a946b13c..636f5fcc986 100644
--- a/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_hierarchy_2.h
+++ b/Triangulation_2/test/Triangulation_2/include/CGAL/_test_cls_hierarchy_2.h
@@ -1,4 +1,4 @@
-#include <CGAL/Constraint_hierarchy_2.h>
+#include <CGAL/Triangulation_2/internal/Constraint_hierarchy_2.h>
 
 struct Less
 {
diff --git a/Triangulation_2/test/Triangulation_2/test_delaunay_triangulation_proj.cpp b/Triangulation_2/test/Triangulation_2/test_delaunay_triangulation_proj.cpp
index 2555f875352..45147e9ea38 100644
--- a/Triangulation_2/test/Triangulation_2/test_delaunay_triangulation_proj.cpp
+++ b/Triangulation_2/test/Triangulation_2/test_delaunay_triangulation_proj.cpp
@@ -1,6 +1,3 @@
-// This file tests the deprecated headers
-// Triangulation_euclidean_traits_.._3 on purpose.
-
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Projection_traits_xy_3.h>
 #include <CGAL/Projection_traits_yz_3.h>