diff --git a/Mesh_3/doc/Mesh_3/Mesh_3.txt b/Mesh_3/doc/Mesh_3/Mesh_3.txt
index 137a81c6d1a..9178befc0db 100644
--- a/Mesh_3/doc/Mesh_3/Mesh_3.txt
+++ b/Mesh_3/doc/Mesh_3/Mesh_3.txt
@@ -677,9 +677,10 @@ View of 3D meshes produced from a polyhedral domain with a nested surface.
 \subsubsection Mesh_3RemeshingPolyhedralSurface Remeshing a Polyhedral Surface
 
 The following code creates a polyhedral domain, with only one polyhedron,
-and no "bounding polyhedron". Since the volumetric part of the domain may be empty,
-and should not be meshed,
-it is necessary to use the `CGAL::parameters::surface_only()` parameter to mesh the surface only.
+and no "bounding polyhedron". The volumetric part of the domain may be empty
+and should not be meshed.
+In this case, it is recommended to use the `CGAL::parameters::surface_only()` parameter
+to speedup the meshing of the surface only.
 This enables to remesh a surface, and is equivalent to the function `make_surface_mesh()`.
 
 \cgalExample{Mesh_3/remesh_polyhedral_surface.cpp}
diff --git a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
index a4a9f49156c..ff76aaea81d 100644
--- a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_3.h
@@ -121,6 +121,10 @@ several other components (closed or not)
 that will be represented in the final mesh.
 This class is a model of the concept `MeshDomain_3`.
 
+\note When the given surface(s) are not closed, the surface only will be meshed.
+It is then recommended to use the parameter `parameters::surface_only()` to speedup
+the meshing process.
+
 \tparam Polyhedron stands for the type of the input polyhedral surface(s),
 model of `FaceListGraph`.
 
@@ -239,11 +243,11 @@ public:
   /// @{
 
   /*!
-    Construction from a polyhedral surface which must and free of intersections.
-    If `polyhedron` is closed, the inside of `bounding_polyhedron` will be meshed,
+    Construction from a polyhedral surface which must be free of intersections.
+    If `polyhedron` is closed, its inside will be meshed,
     otherwise there will be no interior and only the surface will be meshed.
   */
-  Polyhedral_mesh_domain_3(const Polyhedron& bounding_polyhedron
+  Polyhedral_mesh_domain_3(const Polyhedron& polyhedron
 #ifndef DOXYGEN_RUNNING
                            , CGAL::Random* p_rng = nullptr
 #endif
@@ -252,14 +256,14 @@ public:
     , bounding_tree_(&tree_) // the bounding tree is tree_
     , p_rng_(p_rng)
   {
-    this->add_primitives(bounding_polyhedron);
-    if(! is_triangle_mesh(bounding_polyhedron)) {
+    this->add_primitives(polyhedron);
+    if(!is_triangle_mesh(polyhedron)) {
       std::cerr << "Your input polyhedron must be triangulated!\n";
       CGAL_error_msg("Your input polyhedron must be triangulated!");
     }
     this->build();
 
-    if(!is_closed(bounding_polyhedron))
+    if(!is_closed(polyhedron))
       set_surface_only();
   }
 
diff --git a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h
index f6e8bf43d24..2612b3f0828 100644
--- a/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h
+++ b/Mesh_3/include/CGAL/Polyhedral_mesh_domain_with_features_3.h
@@ -72,6 +72,10 @@ It is a model of the concept `MeshDomainWithFeatures_3`. It also provides
 a member function to automatically detect sharp features and boundaries from
 the input polyhedral surface(s).
 
+\note When the given surface(s) are not closed, the surface only will be meshed.
+It is then recommended to use the parameter `parameters::surface_only()` to speedup
+the meshing process.
+
 \tparam IGT stands for a geometric traits class providing the types
 and functors required to implement the intersection tests and intersection computations
 for polyhedral boundary surfaces. This parameter has to be
@@ -162,11 +166,12 @@ public:
 
   /*!
     Constructor from a polyhedral surface.
-    No feature detection is done at this level. Note that a copy of `bounding_polyhedron` will be done.
-    The polyhedron `bounding_polyhedron` has to be closed and free of intersections.
-    The interior of `bounding_polyhedron` will be meshed.
+    No feature detection is done at this level. Note that a copy of `polyhedron` will be done.
+    The polyhedron `polyhedron` must be free of intersections.
+    If `polyhedron` is closed, its inside will be meshed,
+    otherwise there will be no interior and only the surface will be meshed.
   */
-  Polyhedral_mesh_domain_with_features_3(const Polyhedron& bounding_polyhedron
+  Polyhedral_mesh_domain_with_features_3(const Polyhedron& polyhedron
 #ifndef DOXYGEN_RUNNING
                                          , CGAL::Random* p_rng = nullptr
 #endif
@@ -174,10 +179,13 @@ public:
     : Base(p_rng) , borders_detected_(false)
   {
     stored_polyhedra.resize(1);
-    stored_polyhedra[0] = bounding_polyhedron;
+    stored_polyhedra[0] = polyhedron;
     get(face_patch_id_t<Patch_id>(), stored_polyhedra[0]);
     this->add_primitives(stored_polyhedra[0]);
     this->build();
+
+    if(!is_closed(polyhedron))
+      set_surface_only();
   }
 
 #ifndef CGAL_NO_DEPRECATED_CODE