diff --git a/Generator/examples/Generator/random_points_on_triangle_mesh_2.cpp b/Generator/examples/Generator/random_points_on_triangle_mesh_2.cpp
index 5f25f7ba78d..a4b2dd69a81 100644
--- a/Generator/examples/Generator/random_points_on_triangle_mesh_2.cpp
+++ b/Generator/examples/Generator/random_points_on_triangle_mesh_2.cpp
@@ -44,7 +44,8 @@ int main()
   cdt.insert_constraint(polygon2.vertices_begin(), polygon2.vertices_end(), true);
 
   // Refine the triangulation (and mark the faces as inside/outside)
-  CGAL::refine_Delaunay_mesh_2(cdt, Mesh_2_criteria(0.125, 0.5));
+  Mesh_2_criteria criteria(0.125, 0.5);
+  CGAL::refine_Delaunay_mesh_2(cdt, CGAL::parameters::criteria(criteria));
 
   // Create the generator, input is the Triangulation_2 cdt
   Random_points_in_triangle_mesh_2<Point, CDT> g(cdt);
diff --git a/Generator/test/Generator/generic_random_test.cpp b/Generator/test/Generator/generic_random_test.cpp
index eeaad9c012e..2680e0b067c 100644
--- a/Generator/test/Generator/generic_random_test.cpp
+++ b/Generator/test/Generator/generic_random_test.cpp
@@ -157,7 +157,8 @@ int test_T2(const FT eps)
   cdt.insert(Point_2(-1,3));
 
   // Refine the triangulation
-  CGAL::refine_Delaunay_mesh_2(cdt, Mesh_2_criteria(0.125, 0.5));
+  Mesh_2_criteria criteria(0.125, 0.5);
+  CGAL::refine_Delaunay_mesh_2(cdt, CGAL::parameters::criteria(criteria));
 
   CGAL::Random_points_in_triangle_mesh_2<Point_2, CDT> g(cdt);
   std::copy_n(g, 300, std::back_inserter(points));
diff --git a/Mesh_2/test/Mesh_2/test_mesh_projection_traits.cpp b/Mesh_2/test/Mesh_2/test_mesh_projection_traits.cpp
index 63ed376d7af..3138eb37814 100644
--- a/Mesh_2/test/Mesh_2/test_mesh_projection_traits.cpp
+++ b/Mesh_2/test/Mesh_2/test_mesh_projection_traits.cpp
@@ -37,7 +37,8 @@ int main()
   std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
 
   std::cout << "Meshing the triangulation..." << std::endl;
-  CGAL::refine_Delaunay_mesh_2(cdt, Criteria(0.125, 0.5, gt));
+  Criteria criteria(0.125, 0.5, gt);
+  CGAL::refine_Delaunay_mesh_2(cdt, CGAL::parameters::criteria(criteria));
 
   std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
 }
diff --git a/Mesh_2/test/Mesh_2/test_mesh_terrain.cpp b/Mesh_2/test/Mesh_2/test_mesh_terrain.cpp
index fde383f17ca..4ac052fab12 100644
--- a/Mesh_2/test/Mesh_2/test_mesh_terrain.cpp
+++ b/Mesh_2/test/Mesh_2/test_mesh_terrain.cpp
@@ -34,7 +34,8 @@ int main()
   dt.insert_constraint(vc, vd);
   dt.insert_constraint(vd, va);
 
-  CGAL::refine_Delaunay_mesh_2(dt, Criteria(0.125, 0.5));
+  Criteria criteria(0.125, 0.5);
+  CGAL::refine_Delaunay_mesh_2(dt, CGAL::parameters::criteria(criteria));
   // dt.insert(begin, end);
   std::cout << dt.number_of_vertices() << std::endl;
   return 0;
diff --git a/Mesh_2/test/Mesh_2/test_meshing.cpp b/Mesh_2/test/Mesh_2/test_meshing.cpp
index 76c1eb8fa46..ab132707fb9 100644
--- a/Mesh_2/test/Mesh_2/test_meshing.cpp
+++ b/Mesh_2/test/Mesh_2/test_meshing.cpp
@@ -72,8 +72,8 @@ struct Tester2 {
 
     std::cerr << "Meshing the triangulation with size 0...";
     CGAL::refine_Delaunay_mesh_2(cdt,
-                                 seeds.begin(), seeds.end(),
-                                 Criteria());
+                                 CGAL::parameters::seeds(seeds)
+                                 .criteria(Criteria()));
     const size_type number_of_vertices0 = cdt.number_of_vertices();
     std::cerr << " done.\nNumber of vertices: " << cdt.number_of_vertices() << "\n\n";
     assert( 64 <= cdt.number_of_vertices() &&
@@ -82,8 +82,8 @@ struct Tester2 {
 
     std::cerr << "Meshing the triangulation with size 0.2...";
     CGAL::refine_Delaunay_mesh_2(cdt,
-                                 seeds.begin(), seeds.end(),
-                                 Criteria(0.125, 0.2));
+                                 CGAL::parameters::seeds(seeds)
+                                 .criteria(Criteria(0.125, 0.2)));
 
     std::cerr << " done.\nNumber of vertices: " << cdt.number_of_vertices() << "\n\n";
     assert( 190 <= cdt.number_of_vertices() &&
@@ -91,8 +91,8 @@ struct Tester2 {
 
     std::cerr << "Meshing the triangulation with size 0.1...";
     CGAL::refine_Delaunay_mesh_2(cdt,
-                                 seeds.begin(), seeds.end(),
-                                 Criteria(0.125, 0.1));
+                                 CGAL::parameters::seeds(seeds)
+                                 .criteria(Criteria(0.125, 0.1)));
     const size_type number_of_vertices1 = cdt.number_of_vertices();
     std::cerr << " done.\nNumber of vertices: " << cdt.number_of_vertices() << "\n\n";
     assert( 580 <= cdt.number_of_vertices() &&
@@ -104,8 +104,8 @@ struct Tester2 {
 
     std::cerr << "Meshing the triangulation with Delaunay_mesh_criteria_2<CDT>()...";
     CGAL::refine_Delaunay_mesh_2(cdt,
-                                 seeds.begin(), seeds.end(),
-                                 CGAL::Delaunay_mesh_criteria_2<CDT>());
+                                 CGAL::parameters::seeds(seeds).
+                                 criteria(CGAL::Delaunay_mesh_criteria_2<CDT>()));
     const size_type number_of_vertices0bis = cdt.number_of_vertices();
     std::cerr << " done.\nNumber of vertices: " << cdt.number_of_vertices() << "\n\n";
 
@@ -121,8 +121,8 @@ struct Tester2 {
     std::cerr << "Meshing the triangulation with size 0.1, with "
               << "refine_Delaunay_mesh_2()...";
     CGAL::refine_Delaunay_mesh_2(cdt,
-                                 seeds.begin(), seeds.end(),
-                                 Criteria(0.125, 0.1));
+                                 CGAL::parameters::seeds(seeds)
+                                 .criteria(Criteria(0.125, 0.1)));
     const size_type number_of_vertices1bis = cdt.number_of_vertices();
     std::cerr << " done.\nNumber of vertices: " << cdt.number_of_vertices()
               << "\n\n";
diff --git a/Mesh_2/test/Mesh_2/test_meshing_user_bug_test_case.cpp b/Mesh_2/test/Mesh_2/test_meshing_user_bug_test_case.cpp
index 296d8020ce9..b6922b5fee7 100644
--- a/Mesh_2/test/Mesh_2/test_meshing_user_bug_test_case.cpp
+++ b/Mesh_2/test/Mesh_2/test_meshing_user_bug_test_case.cpp
@@ -57,7 +57,8 @@ int main()
   std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
 
   std::cout << "Meshing the triangulation..." << std::endl;
-  CGAL::refine_Delaunay_mesh_2(cdt, Criteria(0.125, 1.0));
+  Criteria criteria(0.125, 0.5);
+  CGAL::refine_Delaunay_mesh_2(cdt, CGAL::parameters::criteria(criteria));
 
   std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
 }