diff --git a/BGL/doc/BGL/CGAL/boost/graph/Named_function_parameters.h b/BGL/doc/BGL/CGAL/boost/graph/Named_function_parameters.h
new file mode 100644
index 00000000000..b3586456dac
--- /dev/null
+++ b/BGL/doc/BGL/CGAL/boost/graph/Named_function_parameters.h
@@ -0,0 +1,11 @@
+namespace CGAL{
+namespace parameters {
+/// \ingroup PkgBGLRef
+/// Type of the default named parameter pack
+typedef unspecified_type Default_named_parameters;
+
+/// \ingroup PkgBGLRef
+/// returns a default named parameter type indicating that default values should be used.
+Default_named_parameters use_default_values();
+
+} }
diff --git a/BGL/doc/BGL/NamedParameters.txt b/BGL/doc/BGL/NamedParameters.txt
index 70a9e8a8029..5a6149f26ce 100644
--- a/BGL/doc/BGL/NamedParameters.txt
+++ b/BGL/doc/BGL/NamedParameters.txt
@@ -24,7 +24,7 @@ The named parameters in the snippet use the tags `predecessor_map` and `distance
 and they are concatenated using the dot operator.<BR>
 
 A similar mechanism was introduced in \cgal, with the small difference that the named parameters
-tag live in the `CGAL::parameters::` namespace and `CGAL::parameters::all_default()` can be used to indicate
+tag live in the `CGAL::parameters::` namespace and `CGAL::parameters::use_default_values()` can be used to indicate
 that default values of optional named parameters must be used.
 As in the \bgl, named parameters in \cgal are also concatenated using
 the dot operator, and a typical usage is thus:
@@ -40,7 +40,9 @@ CGAL::copy_face_graph(g1, g2);
 CGAL::copy_face_graph(g1, g2,
                       CGAL::parameters::vertex_point_map(vpm)  //parameter for g1
                       .vertex_to_vertex_map(v2v),              //other parameter for g1
-                      CGAL::parameters::all_default());        //parameter for g2
+                      CGAL::parameters::use_default_values());        //parameter for g2
 \endcode
 */
+
+
 ˛
diff --git a/BGL/doc/BGL/PackageDescription.txt b/BGL/doc/BGL/PackageDescription.txt
index d74834a3c19..16117666e7c 100644
--- a/BGL/doc/BGL/PackageDescription.txt
+++ b/BGL/doc/BGL/PackageDescription.txt
@@ -683,6 +683,8 @@ user might encounter.
 
 - `CGAL::set_triangulation_ids()`
 
+- `CGAL::parameters::use_default_values()`
+
 \cgalCRPSection{Iterators}
 - `CGAL::Halfedge_around_source_iterator`
 - `CGAL::Halfedge_around_target_iterator`
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
index 8d561e377f2..276192739ea 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
@@ -1106,7 +1106,7 @@ double approximate_Hausdorff_distance(
  *   \cgalParamNEnd
  * \cgalNamedParamsEnd
  *
- * The function `CGAL::parameters::all_default()` can be used to indicate to use the default values
+ * The function `CGAL::parameters::use_default_values()` can be used to indicate to use the default values
  * for `np1` and specify custom values for `np2`.
  */
 template< class Concurrency_tag,
diff --git a/Polygon_mesh_processing/include/CGAL/polygon_mesh_processing.h b/Polygon_mesh_processing/include/CGAL/polygon_mesh_processing.h
index dcea23d7177..d34c23cc378 100644
--- a/Polygon_mesh_processing/include/CGAL/polygon_mesh_processing.h
+++ b/Polygon_mesh_processing/include/CGAL/polygon_mesh_processing.h
@@ -56,6 +56,8 @@ namespace CGAL {
 namespace Polygon_mesh_processing {
 namespace parameters {
 
+/// TODO: remove this one and deprecate it
+
 /*! \ingroup namedparameters
 This function can be used to indicate that all optional named parameters
 to be used are the default ones. This is particularly useful when a function
diff --git a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_class_interface_example.cpp b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_class_interface_example.cpp
index 965a56e30a9..802f06fe8d9 100644
--- a/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_class_interface_example.cpp
+++ b/Surface_mesh_approximation/examples/Surface_mesh_approximation/vsa_class_interface_example.cpp
@@ -61,7 +61,7 @@ int main(int argc, char** argv)
   approx.run(10);
 
   // extract approximated mesh with default parameters
-  approx.extract_mesh(CGAL::parameters::all_default());
+  approx.extract_mesh(CGAL::parameters::use_default_values());
 
   // get approximated triangle soup
   std::vector<Kernel::Point_3> anchors;
diff --git a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h
index f7dbb84e459..6e3bb125095 100644
--- a/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h
+++ b/Surface_mesh_approximation/include/CGAL/Surface_mesh_approximation/approximate_triangle_mesh.h
@@ -43,18 +43,6 @@ enum Verbose_level {
   VERBOSE
 };
 
-// the named parameter header being not documented the doc is put here for now
-#ifdef DOXYGEN_RUNNING
-namespace parameters {
-
-/*! \ingroup bgl_namedparameters
- * This function is used when default parameters are just fine for approximation or meshing.
- */
-unspecified_type all_default();
-
-} // namespace parameters
-#endif
-
 /*!
  * \ingroup PkgTSMARef
  * @brief approximates the input mesh with plane proxies.