diff --git a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_projection_traits.cpp b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_projection_traits.cpp
index c2adfce40a1..bdc7e8a1516 100644
--- a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_projection_traits.cpp
+++ b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_projection_traits.cpp
@@ -57,6 +57,8 @@ private:
 
 // The partial specialization must be defined before Alpha Shapes-related headers
 #include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
 
 // ExactAlphaComparisonTag is false
 typedef K Gt;
diff --git a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp
index 0fd24993b5d..505c2bcac4e 100644
--- a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp
+++ b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_alpha_shapes_2.cpp
@@ -1,12 +1,17 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/algorithm.h>
-#include <CGAL/Delaunay_triangulation_2.h>
-#include <CGAL/Alpha_shape_2.h>
 
-#include <iostream>
+#include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
+#include <CGAL/Delaunay_triangulation_2.h>
+
+#include <CGAL/algorithm.h>
+#include <CGAL/assertions.h>
+
 #include <fstream>
-#include <vector>
+#include <iostream>
 #include <list>
+#include <vector>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel  K;
 
diff --git a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_weighted_alpha_shapes_2.cpp b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_weighted_alpha_shapes_2.cpp
index bb7112c924a..5e9fa6ad099 100644
--- a/Alpha_shapes_2/examples/Alpha_shapes_2/ex_weighted_alpha_shapes_2.cpp
+++ b/Alpha_shapes_2/examples/Alpha_shapes_2/ex_weighted_alpha_shapes_2.cpp
@@ -1,11 +1,14 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
-#include <CGAL/Regular_triangulation_2.h>
-#include <CGAL/Alpha_shape_2.h>
 
-#include <iostream>
+#include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
+#include <CGAL/Regular_triangulation_2.h>
+
 #include <fstream>
-#include <vector>
+#include <iostream>
 #include <list>
+#include <vector>
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 
diff --git a/Alpha_shapes_2/include/CGAL/Alpha_shape_2.h b/Alpha_shapes_2/include/CGAL/Alpha_shape_2.h
index 7f72073acc8..af575b1d0bd 100644
--- a/Alpha_shapes_2/include/CGAL/Alpha_shape_2.h
+++ b/Alpha_shapes_2/include/CGAL/Alpha_shape_2.h
@@ -12,10 +12,6 @@
 // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 //
-// $URL$
-// $Id$
-// 
-//
 // Author(s)     : Tran Kai Frank DA
 //                 Andreas Fabri <Andreas.Fabri@geometryfactory.com>
 
@@ -24,31 +20,30 @@
 
 #include <CGAL/license/Alpha_shapes_2.h>
 
-
-#include <CGAL/basic.h>
-
-#include <list>
-#include <set>
-#include <map>
-#include <vector>
-#include <algorithm>
-#include <utility>
-#include <iostream>
-
-#include <CGAL/utility.h>
-#include <CGAL/Unique_hash_map.h>
-#include <CGAL/Triangulation_vertex_base_2.h>
-#include <CGAL/Triangulation_face_base_2.h>
-#include <CGAL/Alpha_shape_vertex_base_2.h>
-#include <CGAL/Alpha_shape_face_base_2.h>
 #include <CGAL/internal/Lazy_alpha_nt_2.h>
 
+// for convenience only
+#include <CGAL/Alpha_shape_vertex_base_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
 
+#include <CGAL/assertions.h>
+#include <CGAL/basic.h>
+#include <CGAL/triangulation_assertions.h>
+#include <CGAL/Unique_hash_map.h>
+#include <CGAL/utility.h>
+
+#include <algorithm>
+#include <iostream>
+#include <list>
+#include <map>
+#include <set>
+#include <utility>
+#include <vector>
 
 namespace CGAL {
 
 template < class Dt,class ExactAlphaComparisonTag = Tag_false>
-class Alpha_shape_2 : public Dt 
+class Alpha_shape_2 : public Dt
 {
   // DEFINITION The class Alpha_shape_2<Dt> represents the family
   // of alpha-shapes of points in a plane for all positive alpha. It
diff --git a/Alpha_shapes_2/test/Alpha_shapes_2/test_alpha.cpp b/Alpha_shapes_2/test/Alpha_shapes_2/test_alpha.cpp
index 251a01b4bf5..715416fc3b5 100644
--- a/Alpha_shapes_2/test/Alpha_shapes_2/test_alpha.cpp
+++ b/Alpha_shapes_2/test/Alpha_shapes_2/test_alpha.cpp
@@ -8,8 +8,10 @@
 #include <vector>
 #include <list>
 
-#include <CGAL/Delaunay_triangulation_2.h>
 #include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
+#include <CGAL/Delaunay_triangulation_2.h>
 
 typedef double coord_type;
 
diff --git a/Alpha_shapes_2/test/Alpha_shapes_2/test_weight.cpp b/Alpha_shapes_2/test/Alpha_shapes_2/test_weight.cpp
index 1ddbf60b5a4..17a441b1978 100644
--- a/Alpha_shapes_2/test/Alpha_shapes_2/test_weight.cpp
+++ b/Alpha_shapes_2/test/Alpha_shapes_2/test_weight.cpp
@@ -7,15 +7,18 @@ corresponding to the weighted Alpha Shape.
 
 #include <CGAL/Simple_cartesian.h>
 #include <CGAL/Filtered_kernel.h>
+
+#include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
+#include <CGAL/Regular_triangulation_2.h>
+
 #include <cstdio>
 #include <cstring>
-#include <iostream>
 #include <fstream>
-#include <vector>
+#include <iostream>
 #include <list>
-
-#include <CGAL/Regular_triangulation_2.h>
-#include <CGAL/Alpha_shape_2.h>
+#include <vector>
 
 typedef double                                          coord_type;
 
diff --git a/Alpha_shapes_3/include/CGAL/Alpha_shape_3.h b/Alpha_shapes_3/include/CGAL/Alpha_shape_3.h
index c1ec0c05ca6..8a7b13a9e1b 100644
--- a/Alpha_shapes_3/include/CGAL/Alpha_shape_3.h
+++ b/Alpha_shapes_3/include/CGAL/Alpha_shape_3.h
@@ -12,10 +12,6 @@
 // This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 // WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 //
-// $URL$
-// $Id$
-// 
-//
 // Author(s)     : Tran Kai Frank DA <Frank.Da@sophia.inria.fr>
 //                 Andreas Fabri <Andreas.Fabri@geometryfactory.com>
 //                 Mariette Yvinec <Mariette.Yvinec@sophia.inria.fr>
@@ -25,28 +21,27 @@
 
 #include <CGAL/license/Alpha_shapes_3.h>
 
+#include <CGAL/internal/Lazy_alpha_nt_3.h>
 
 #include <CGAL/basic.h>
-
-#include <set>
-#include <map>
-#include <list>
-#include <vector>
-#include <algorithm>
-#include <utility>
-#include <iostream>
-
-#include <CGAL/Triangulation_utils_3.h>
+#include <CGAL/Compact_container.h>
+#include <CGAL/iterator.h>
 #include <CGAL/Object.h>
 #include <CGAL/Unique_hash_map.h>
-#include <CGAL/Compact_container.h>
-#include <CGAL/Alpha_shape_vertex_base_3.h>
-#include <CGAL/Alpha_shape_cell_base_3.h>
-#include <CGAL/internal/Lazy_alpha_nt_3.h>
-#include <CGAL/iterator.h>
 #ifdef CGAL_USE_GEOMVIEW
 #include <CGAL/IO/Geomview_stream.h>  // TBC
 #endif
+#include <CGAL/Triangulation_utils_3.h>
+
+#include <boost/type_traits/is_same.hpp>
+
+#include <algorithm>
+#include <iostream>
+#include <map>
+#include <list>
+#include <set>
+#include <utility>
+#include <vector>
 
 //-------------------------------------------------------------------
 namespace CGAL {
diff --git a/CGAL_ipelets/demo/CGAL_ipelets/alpha_shapes.cpp b/CGAL_ipelets/demo/CGAL_ipelets/alpha_shapes.cpp
index defdb229844..b80ab1330ce 100644
--- a/CGAL_ipelets/demo/CGAL_ipelets/alpha_shapes.cpp
+++ b/CGAL_ipelets/demo/CGAL_ipelets/alpha_shapes.cpp
@@ -24,6 +24,8 @@
 #include <CGAL/Constrained_Delaunay_triangulation_2.h>
 #include <CGAL/Delaunay_triangulation_2.h>
 #include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
 #include <boost/format.hpp>
 
 
diff --git a/GraphicsView/demo/Alpha_shapes_2/Alpha_shapes_2.cpp b/GraphicsView/demo/Alpha_shapes_2/Alpha_shapes_2.cpp
index 4d85393bbdc..b1f1b3c11b0 100644
--- a/GraphicsView/demo/Alpha_shapes_2/Alpha_shapes_2.cpp
+++ b/GraphicsView/demo/Alpha_shapes_2/Alpha_shapes_2.cpp
@@ -4,6 +4,8 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 #include <CGAL/Delaunay_triangulation_2.h>
 #include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
 
 #include <CGAL/point_generators_2.h>
 
diff --git a/Polyhedron/demo/Polyhedron/Plugins/Point_set/Point_set_shape_detection_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/Point_set/Point_set_shape_detection_plugin.cpp
index fff6287c3bb..a605661d763 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/Point_set/Point_set_shape_detection_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/Point_set/Point_set_shape_detection_plugin.cpp
@@ -23,6 +23,8 @@
 #include <CGAL/regularize_planes.h>
 #include <CGAL/Delaunay_triangulation_2.h>
 #include <CGAL/Alpha_shape_2.h>
+#include <CGAL/Alpha_shape_face_base_2.h>
+#include <CGAL/Alpha_shape_vertex_base_2.h>
 
 #include <CGAL/structure_point_set.h>