diff --git a/Installation/changes.html b/Installation/changes.html
index ae1f7c88017..e0431913e24 100644
--- a/Installation/changes.html
+++ b/Installation/changes.html
@@ -285,6 +285,9 @@ and <code>src/</code> directories).
      <code>max_distance_to_triangle_mesh()</code>,
      <code>max_distance_to_point_set()</code>.
     </li>
+    <li>
+    The function <code>CGAL::Polygon_mesh_processing::bbox_3()</code> has been renamed <code>CGAL::Polygon_mesh_processing::bbox()</code>.
+    </li>
   </ul>
 
   <h3>Point Set Processing</h3>
diff --git a/Polygon_mesh_processing/doc/Polygon_mesh_processing/PackageDescription.txt b/Polygon_mesh_processing/doc/Polygon_mesh_processing/PackageDescription.txt
index 7d0dd6a2cec..11ee3686682 100644
--- a/Polygon_mesh_processing/doc/Polygon_mesh_processing/PackageDescription.txt
+++ b/Polygon_mesh_processing/doc/Polygon_mesh_processing/PackageDescription.txt
@@ -153,10 +153,10 @@ and provides a list of the parameters that are used in this package.
 ## Miscellaneous ##
 - `CGAL::Polygon_mesh_slicer`
 - `CGAL::Side_of_triangle_mesh`
-- `CGAL::Polygon_mesh_processing::bbox_3()`
-- `CGAL::Polygon_mesh_processing::vertex_bbox_3()`
-- `CGAL::Polygon_mesh_processing::edge_bbox_3()`
-- `CGAL::Polygon_mesh_processing::face_bbox_3()`
+- `CGAL::Polygon_mesh_processing::bbox()`
+- `CGAL::Polygon_mesh_processing::vertex_bbox()`
+- `CGAL::Polygon_mesh_processing::edge_bbox()`
+- `CGAL::Polygon_mesh_processing::face_bbox()`
 - `CGAL::Polygon_mesh_processing::border_halfedges()`
 
 \todo add `clip_triangle_mesh()` using the code of `Polyhedron_place_clipping.h` and `PMP::corefine()`
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
index 1f5fd89ae96..9fa7730f52b 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/bbox.h
@@ -62,8 +62,8 @@ namespace CGAL {
     * @return a bounding box of `pmesh`
     */
     template<typename PolygonMesh, typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
-    CGAL::Bbox_3 bbox_3(const PolygonMesh& pmesh,
-                        const CGAL_PMP_NP_CLASS& np)
+    CGAL::Bbox_3 bbox(const PolygonMesh& pmesh,
+                      const CGAL_PMP_NP_CLASS& np)
     {
       using boost::choose_param;
       using boost::get_param;
@@ -112,9 +112,9 @@ namespace CGAL {
     * @return a bounding box of `pmesh`
     */
     template<typename PolygonMesh, typename NamedParameters>
-    CGAL::Bbox_3 vertex_bbox_3(typename boost::graph_traits<PolygonMesh>::vertex_descriptor vd,
-                               const PolygonMesh& pmesh,
-                               const NamedParameters& np)
+    CGAL::Bbox_3 vertex_bbox(typename boost::graph_traits<PolygonMesh>::vertex_descriptor vd,
+                             const PolygonMesh& pmesh,
+                             const NamedParameters& np)
     {
       using boost::choose_param;
       using boost::get_param;
@@ -155,9 +155,9 @@ namespace CGAL {
     * @return a bounding box of `pmesh`
     */
     template<typename PolygonMesh, typename NamedParameters>
-    CGAL::Bbox_3 edge_bbox_3(typename boost::graph_traits<PolygonMesh>::edge_descriptor ed,
-                             const PolygonMesh& pmesh,
-                             const NamedParameters& np)
+    CGAL::Bbox_3 edge_bbox(typename boost::graph_traits<PolygonMesh>::edge_descriptor ed,
+                           const PolygonMesh& pmesh,
+                           const NamedParameters& np)
     {
       using boost::choose_param;
       using boost::get_param;
@@ -199,9 +199,9 @@ namespace CGAL {
     * @return a bounding box of `pmesh`
     */
     template<typename PolygonMesh, typename NamedParameters>
-    CGAL::Bbox_3 face_bbox_3(typename boost::graph_traits<PolygonMesh>::face_descriptor fd,
-                             const PolygonMesh& pmesh,
-                             const NamedParameters& np)
+    CGAL::Bbox_3 face_bbox(typename boost::graph_traits<PolygonMesh>::face_descriptor fd,
+                           const PolygonMesh& pmesh,
+                           const NamedParameters& np)
     {
       using boost::choose_param;
       using boost::get_param;
@@ -225,34 +225,53 @@ namespace CGAL {
     }
 
     template<typename PolygonMesh>
-    CGAL::Bbox_3 vertex_bbox_3(typename boost::graph_traits<PolygonMesh>::vertex_descriptor vd,
+    CGAL::Bbox_3 vertex_bbox(typename boost::graph_traits<PolygonMesh>::vertex_descriptor vd,
                                const PolygonMesh& pmesh)
     {
-      return vertex_bbox_3(vd, pmesh,
+      return vertex_bbox(vd, pmesh,
         CGAL::Polygon_mesh_processing::parameters::all_default());
     }
     template<typename PolygonMesh>
-    CGAL::Bbox_3 edge_bbox_3(typename boost::graph_traits<PolygonMesh>::edge_descriptor ed,
+    CGAL::Bbox_3 edge_bbox(typename boost::graph_traits<PolygonMesh>::edge_descriptor ed,
                              const PolygonMesh& pmesh)
     {
-      return edge_bbox_3(ed, pmesh,
+      return edge_bbox(ed, pmesh,
         CGAL::Polygon_mesh_processing::parameters::all_default());
     }
     template<typename PolygonMesh>
-    CGAL::Bbox_3 face_bbox_3(typename boost::graph_traits<PolygonMesh>::face_descriptor fd,
+    CGAL::Bbox_3 face_bbox(typename boost::graph_traits<PolygonMesh>::face_descriptor fd,
                              const PolygonMesh& pmesh)
     {
-      return face_bbox_3(fd, pmesh,
+      return face_bbox(fd, pmesh,
         CGAL::Polygon_mesh_processing::parameters::all_default());
     }
 
     template<typename PolygonMesh>
-    CGAL::Bbox_3 bbox_3(const PolygonMesh& pmesh)
+    CGAL::Bbox_3 bbox(const PolygonMesh& pmesh)
     {
-      return bbox_3(pmesh,
+      return bbox(pmesh,
         CGAL::Polygon_mesh_processing::parameters::all_default());
     }
 
+    // deprecated function
+    #ifndef CGAL_NO_DEPRECATED_CODE
+    /*!
+    * \ingroup PkgPolygonMeshProcessing
+    * \deprecated This function is deprecated since \cgal 4.10, `CGAL::Polygon_mesh_processing::bbox()` should be used instead.
+    */
+    template<typename PolygonMesh, typename CGAL_PMP_NP_TEMPLATE_PARAMETERS>
+    CGAL_DEPRECATED CGAL::Bbox_3 bbox_3(const PolygonMesh& pmesh,
+                        const CGAL_PMP_NP_CLASS& np)
+    {
+      return bbox(pmesh, np);
+    }
+
+    template<typename PolygonMesh>
+    CGAL_DEPRECATED CGAL::Bbox_3 bbox_3(const PolygonMesh& pmesh)
+    {
+      return bbox(pmesh);
+    }
+    #endif // CGAL_NO_DEPRECATED_CODE
   }
 }
 
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/clip.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/clip.h
index 1ba7a85dcdb..f5af2d6bc69 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/clip.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/clip.h
@@ -341,7 +341,7 @@ void clip(      TriangleMesh& tm,
           bool close)
 {
   if( boost::begin(faces(tm))==boost::end(faces(tm)) ) return;
-  CGAL::Bbox_3 bbox = bbox_3(tm);
+  CGAL::Bbox_3 bbox = ::CGAL::Polygon_mesh_processing::bbox(tm);
   //extend the bbox a bit to avoid border cases
   double xd=(bbox.xmax()-bbox.xmin())/100;
   double yd=(bbox.ymax()-bbox.ymin())/100;
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp
index 16092ffcd22..2f57d425230 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp
@@ -95,22 +95,22 @@ void test_pmesh(const Mesh& pmesh)
   std::cout << "mesh area (NP) = " << mesh_area_np << std::endl;
 
 
-  CGAL::Bbox_3 bb = PMP::bbox_3(pmesh);
+  CGAL::Bbox_3 bb = PMP::bbox(pmesh);
   std::cout << "bbox x[" << bb.xmin() << "; " << bb.xmax() << "]" << std::endl;
   std::cout << "     y[" << bb.ymin() << "; " << bb.ymax() << "]" << std::endl;
   std::cout << "     z[" << bb.zmin() << "; " << bb.zmax() << "]" << std::endl;
 
   CGAL::Bbox_3 bb_v;
   BOOST_FOREACH(vertex_descriptor vd, vertices(pmesh))
-    bb_v+=PMP::vertex_bbox_3(vd, pmesh);
+    bb_v+=PMP::vertex_bbox(vd, pmesh);
 
   CGAL::Bbox_3 bb_f;
   BOOST_FOREACH(face_descriptor fd, faces(pmesh))
-    bb_f+=PMP::face_bbox_3(fd, pmesh);
+    bb_f+=PMP::face_bbox(fd, pmesh);
 
   CGAL::Bbox_3 bb_e;
   BOOST_FOREACH(edge_descriptor ed, edges(pmesh))
-    bb_e+=PMP::edge_bbox_3(ed, pmesh);
+    bb_e+=PMP::edge_bbox(ed, pmesh);
 
   assert(bb==bb_v);
   assert(bb==bb_f);
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/point_inside_helpers.h b/Polygon_mesh_processing/test/Polygon_mesh_processing/point_inside_helpers.h
index 8b3b5d5a548..cb8ca41ad26 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/point_inside_helpers.h
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/point_inside_helpers.h
@@ -77,7 +77,7 @@ void random_points(const PolygonMesh& mesh,
                    int n,
                    OutputIterator out)
 {
-  CGAL::Bbox_3 bb = CGAL::Polygon_mesh_processing::bbox_3(mesh);
+  CGAL::Bbox_3 bb = CGAL::Polygon_mesh_processing::bbox(mesh);
   CGAL::Random rg(1340818006); // seed some value for make it easy to debug
 
   double grid_dx = bb.xmax() - bb.xmin();