diff --git a/BGL/include/CGAL/boost/graph/parameters_interface.h b/BGL/include/CGAL/boost/graph/parameters_interface.h
index 8e030bde218..988528cbd4e 100644
--- a/BGL/include/CGAL/boost/graph/parameters_interface.h
+++ b/BGL/include/CGAL/boost/graph/parameters_interface.h
@@ -67,7 +67,7 @@ CGAL_add_named_parameter(preserve_genus_t, preserve_genus, preserve_genus)
 CGAL_add_named_parameter(new_face_visitor_t, new_face_visitor, new_face_visitor)
 CGAL_add_named_parameter(throw_on_self_intersection_t, throw_on_self_intersection, throw_on_self_intersection)
 CGAL_add_named_parameter(clip_volumes_t, clip_volumes, clip_volumes)
-CGAL_add_named_parameter(include_clipper_boundary_t, include_clipper_boundary, include_clipper_boundary)
+CGAL_add_named_parameter(use_compact_clipper_t, use_compact_clipper, use_compact_clipper)
 
 // List of named parameters that we use in the package 'Surface Mesh Simplification'
 CGAL_add_named_parameter(get_cost_policy_t, get_cost_policy, get_cost)
diff --git a/BGL/test/BGL/test_cgal_bgl_named_params.cpp b/BGL/test/BGL/test_cgal_bgl_named_params.cpp
index 73ac8b7331b..ada231d4e3b 100644
--- a/BGL/test/BGL/test_cgal_bgl_named_params.cpp
+++ b/BGL/test/BGL/test_cgal_bgl_named_params.cpp
@@ -75,7 +75,7 @@ void test(const NamedParameters& np)
   assert(get_param(np, CGAL::internal_np::new_face_visitor).v == 42);
   assert(get_param(np, CGAL::internal_np::throw_on_self_intersection).v == 43);
   assert(get_param(np, CGAL::internal_np::clip_volumes).v == 44);
-  assert(get_param(np, CGAL::internal_np::include_clipper_boundary).v == 45);
+  assert(get_param(np, CGAL::internal_np::use_compact_clipper).v == 45);
 
     // Named parameters that we use in the package 'Surface Mesh Simplification'
   assert(get_param(np, CGAL::internal_np::get_cost_policy).v == 34);
@@ -143,7 +143,7 @@ void test(const NamedParameters& np)
   check_same_type<42>(get_param(np, CGAL::internal_np::new_face_visitor));
   check_same_type<43>(get_param(np, CGAL::internal_np::throw_on_self_intersection));
   check_same_type<44>(get_param(np, CGAL::internal_np::clip_volumes));
-  check_same_type<45>(get_param(np, CGAL::internal_np::include_clipper_boundary));
+  check_same_type<45>(get_param(np, CGAL::internal_np::use_compact_clipper));
 
     // Named parameters that we use in the package 'Surface Mesh Simplification'
   check_same_type<34>(get_param(np, CGAL::internal_np::get_cost_policy));
@@ -210,7 +210,7 @@ int main()
                          .new_face_visitor(A<42>(42))
                          .throw_on_self_intersection(A<43>(43))
                          .clip_volumes(A<44>(44))
-                         .include_clipper_boundary(A<45>(45))
+                         .use_compact_clipper(A<45>(45))
        );
 
   return EXIT_SUCCESS;
diff --git a/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt b/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt
index 3f4f0f8c94b..f5d90b55417 100644
--- a/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt
+++ b/Polygon_mesh_processing/doc/Polygon_mesh_processing/NamedParameters.txt
@@ -334,9 +334,9 @@ Parameter used in `clip()` functions to clip a volume rather than a surface.
 \b Default value is `false`
 \cgalNPEnd
 
-\cgalNPBegin{include_clipper_boundary} \anchor PMP_include_clipper_boundary
+\cgalNPBegin{use_compact_clipper} \anchor PMP_use_compact_clipper
 Parameter used in `clip()` functions to indicate whether the boundary of the clipper
-should be considered as part of the volume or not.
+should be considered as part of the clipping volume or not.
 \n
 \b Type : `bool` \n
 \b Default value is `true`
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
index 0f645e0290d..b1ca57869b0 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/clip.h
@@ -146,7 +146,7 @@ clip_open_impl(      TriangleMesh& tm,
   {
     // A patch without no vertex incident to a non-constrained edges
     //  is a coplanar patch: drop it or keep it!
-    if (!boost::choose_param(boost::get_param(np_tm, internal_np::include_clipper_boundary), true))
+    if (!boost::choose_param(boost::get_param(np_tm, internal_np::use_compact_clipper), true))
     {
       for (std::size_t cc_id = cc_not_handled.find_first();
                        cc_id < cc_not_handled.npos;
@@ -312,8 +312,8 @@ clip_to_bbox(const Plane_3& plane,
   *      the volume \link coref_def_subsec bounded \endlink by `tm` rather than on its surface
   *      (i.e. `tm` will be kept closed).
   *   \cgalParamEnd
-  *   \cgalParamBegin{include_clipper_boundary} if `false` and `clip_volumes` is `false` and `tm` is open, the parts of `tm` coplanar with `clipper`
-  *                                             will not be part of the output.
+  *   \cgalParamBegin{use_compact_clipper} if `false` and `clip_volumes` is `false` and `tm` is open, the parts of `tm` coplanar with `clipper`
+  *                                        will not be part of the output.
   *   \cgalParamEnd
   * \cgalNamedParamsEnd
   *
@@ -375,8 +375,8 @@ clip(      TriangleMesh& tm,
   *      the volume \link coref_def_subsec bounded \endlink by `tm` rather than on its surface
   *      (i.e. `tm` will be kept closed).
   *   \cgalParamEnd
-  *   \cgalParamBegin{include_clipper_boundary} if `false` and `clip_volumes` is `false` and `tm` is open, the parts of `tm` coplanar with `plane`
-  *                                             will not be part of the output.
+  *   \cgalParamBegin{use_compact_clipper} if `false` and `clip_volumes` is `false` and `tm` is open, the parts of `tm` coplanar with `plane`
+  *                                        will not be part of the output.
   * \cgalNamedParamsEnd
   *
   * @return `true` if the output surface mesh is manifold.