diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
index 78d8c572e26..761d7f98a77 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/corefinement.h
@@ -90,8 +90,8 @@ enum Boolean_operation_type {UNION = 0, INTERSECTION=1,
   * \pre \link CGAL::Polygon_mesh_processing::does_bound_a_volume() `CGAL::Polygon_mesh_processing::does_bound_a_volume(tm2)` \endlink
   *
   * @tparam TriangleMesh a model of `HalfedgeListGraph`, `FaceListGraph`, and `MutableFaceGraph`
-  * @tparam NamedParameters1 a sequence of \ref bgl_namedparameters "Named Parameters"
-  * @tparam NamedParameters2 a sequence of \ref bgl_namedparameters "Named Parameters"
+  * @tparam NPIn1 a sequence of \ref bgl_namedparameters "Named Parameters"
+  * @tparam NPIn2 a sequence of \ref bgl_namedparameters "Named Parameters"
   * @tparam NPOut0 a sequence of \ref bgl_namedparameters "Named Parameters" for computing the union of the volumes bounded by `tm1` and `tm2`
   * @tparam NPOut1 a sequence of \ref bgl_namedparameters "Named Parameters" for computing the intersection of the volumes bounded by `tm1` and `tm2`
   * @tparam NPOut2 a sequence of \ref bgl_namedparameters "Named Parameters" for computing the difference of the volumes bounded by `tm1` and `tm2`
@@ -176,8 +176,8 @@ enum Boolean_operation_type {UNION = 0, INTERSECTION=1,
   *         will only be corefined.
   */
 template <class TriangleMesh,
-          class NamedParameters1 = parameters::Default_named_parameters,
-          class NamedParameters2 = parameters::Default_named_parameters,
+          class NPIn1 = parameters::Default_named_parameters,
+          class NPIn2 = parameters::Default_named_parameters,
           class NPOut0 = parameters::Default_named_parameters,
           class NPOut1 = parameters::Default_named_parameters,
           class NPOut2 = parameters::Default_named_parameters,
@@ -187,8 +187,8 @@ corefine_and_compute_boolean_operations(
         TriangleMesh& tm1,
         TriangleMesh& tm2,
   const std::array< boost::optional<TriangleMesh*>,4>& output,
-  const NamedParameters1& np1 = parameters::default_values(),
-  const NamedParameters2& np2 = parameters::default_values(),
+  const NPIn1& np1 = parameters::default_values(),
+  const NPIn2& np2 = parameters::default_values(),
   const std::tuple<NPOut0,
                    NPOut1,
                    NPOut2,
@@ -203,8 +203,8 @@ corefine_and_compute_boolean_operations(
 
 // Vertex point maps
   //for input meshes
-  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters1>::type  VPM1;
-  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters2>::type  VPM2;
+  typedef typename GetVertexPointMap<TriangleMesh, NPIn1>::type  VPM1;
+  typedef typename GetVertexPointMap<TriangleMesh, NPIn2>::type  VPM2;
 
   CGAL_static_assertion((std::is_same<typename boost::property_traits<VPM1>::value_type,
                                       typename boost::property_traits<VPM2>::value_type>::value));
@@ -331,13 +331,13 @@ corefine_and_compute_boolean_operations(
   //for input meshes
   typedef typename internal_np::Lookup_named_param_def <
     internal_np::edge_is_constrained_t,
-    NamedParameters1,
+    NPIn1,
     Corefinement::No_mark<TriangleMesh>//default
   > ::type Ecm1;
 
   typedef typename internal_np::Lookup_named_param_def <
     internal_np::edge_is_constrained_t,
-    NamedParameters2,
+    NPIn2,
     Corefinement::No_mark<TriangleMesh>//default
   > ::type Ecm2;
 
@@ -357,8 +357,8 @@ corefine_and_compute_boolean_operations(
                                                             Edge_mark_map_tuple;
 
   // Face index point maps
-  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NamedParameters1>::type FaceIndexMap1;
-  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NamedParameters2>::type FaceIndexMap2;
+  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NPIn1>::type FaceIndexMap1;
+  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NPIn2>::type FaceIndexMap2;
 
   FaceIndexMap1 fid_map1 = get_initialized_face_index_map(tm1, np1);
   FaceIndexMap2 fid_map2 = get_initialized_face_index_map(tm2, np2);
@@ -367,7 +367,7 @@ corefine_and_compute_boolean_operations(
   // User visitor
   typedef typename internal_np::Lookup_named_param_def <
     internal_np::visitor_t,
-    NamedParameters1,
+    NPIn1,
     Corefinement::Default_visitor<TriangleMesh>//default
   > ::type User_visitor;
   User_visitor uv(choose_parameter<User_visitor>(get_parameter(np1, internal_np::visitor)));