diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
index d84974ce78f..3706b1ec196 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
@@ -118,8 +118,7 @@ void poisson_reconstruction(const PointSet& points, const char* output)
   std::cout << "Start meshing...";
   std::cout.flush();
   C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-                                      params::no_exude()
-                                             .no_perturb()
+                                      params::surface_only()
                                              .manifold_with_boundary());
 
   time.stop();
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
index 4e9bdf1360f..82c3a623d2c 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
@@ -332,7 +332,7 @@ int main(int argc, char * argv[])
 
     // Generates mesh with manifold option
     C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-                                        CGAL::parameters::no_exude().no_perturb()
+                                        CGAL::parameters::surface_only()
                                         .manifold_with_boundary());
 
     // Prints status
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
index c73be4427e9..4d4806a7d25 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
@@ -90,7 +90,7 @@ int main(void)
 
     // Generates mesh with manifold option
     C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-                                        CGAL::parameters::no_exude().no_perturb()
+                                        CGAL::parameters::surface_only()
                                         .manifold_with_boundary());
 
     const Tr& tr = c3t3.triangulation();
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h b/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
index 9584e34f59f..fa39d55b131 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
@@ -17,7 +17,7 @@
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
-#include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 #include <CGAL/Poisson_reconstruction_function.h>
@@ -99,7 +99,7 @@ namespace CGAL {
     typedef typename Kernel::FT FT;
 
     typedef CGAL::Poisson_reconstruction_function<Kernel> Poisson_reconstruction_function;
-    typedef CGAL::Labeled_mesh_domain_3<Kernel> Mesh_domain;
+    typedef CGAL::Poisson_mesh_domain_3<Kernel> Mesh_domain;
     typedef typename CGAL::Mesh_triangulation_3<Mesh_domain, CGAL::Default, Sequential_tag>::type Tr;
     typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
     typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
@@ -115,7 +115,7 @@ namespace CGAL {
     FT sm_sphere_radius = 5.0 * radius;
     FT sm_dichotomy_error = sm_distance * spacing / 1000.0;
 
-    Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(function, Sphere(inner_point, sm_sphere_radius),
+    Mesh_domain domain = Mesh_domain::create_Poisson_mesh_domain(function, Sphere(inner_point, sm_sphere_radius),
       CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
     Mesh_criteria criteria(CGAL::parameters::facet_angle = sm_angle,
@@ -134,7 +134,7 @@ namespace CGAL {
 
     C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
                                         turn_tag_into_mesh_3_manifold_option(tag)
-                                        .no_exude().no_perturb()
+                                        .surface_only()
                                         .manifold_with_boundary());
 
     const auto& tr = c3t3.triangulation();
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
index 5fb8c4a34e6..117ccf97729 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
@@ -356,7 +356,7 @@ int main(int argc, char * argv[])
 
       // Generates mesh with manifold option
       LC3t3 c3t3 =
-          CGAL::make_mesh_3<LC3t3>(domain, criteria, CGAL::parameters::no_exude().no_perturb().manifold_with_boundary());
+          CGAL::make_mesh_3<LC3t3>(domain, criteria, CGAL::parameters::surface_only().manifold_with_boundary());
       meshing_timer.stop();
 
       const LTr& tr = c3t3.triangulation();
@@ -398,7 +398,7 @@ int main(int argc, char * argv[])
 
       // Generates mesh with manifold option
       C3t3 c3t3 =
-          CGAL::make_mesh_3<C3t3>(domain, criteria, CGAL::parameters::no_exude().no_perturb().manifold_with_boundary());
+          CGAL::make_mesh_3<C3t3>(domain, criteria, CGAL::parameters::surface_only().manifold_with_boundary());
 
       meshing_timer.stop();
 
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
index f171053e86d..720e3f4b18b 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
@@ -276,7 +276,7 @@ int main(int argc, char * argv[])
       // Generates surface mesh with manifold option
       Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(
           function, bsphere, params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
-      C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, params::no_exude().no_perturb().manifold_with_boundary());
+      C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, params::surface_only().manifold_with_boundary());
 
       // Prints status
       /*long*/ memory = CGAL::Memory_sizer().virtual_size();
@@ -320,7 +320,7 @@ int main(int argc, char * argv[])
       Poisson_mesh_domain domain = Poisson_mesh_domain::create_Poisson_mesh_domain(
           function, bsphere, params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
       Poisson_C3t3 c3t3 =
-          CGAL::make_mesh_3<Poisson_C3t3>(domain, criteria, params::no_exude().no_perturb().manifold_with_boundary());
+          CGAL::make_mesh_3<Poisson_C3t3>(domain, criteria, params::surface_only().manifold_with_boundary());
 
       // Prints status
       /* long */ memory = CGAL::Memory_sizer().virtual_size();