diff --git a/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h b/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h
index 16ffb523203..c3dfdecab30 100644
--- a/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h
+++ b/Mesh_2/include/CGAL/Constrained_voronoi_diagram_2.h
@@ -273,7 +273,7 @@ private:
 
     if(!m_cdt.is_infinite(seed) 
        && !seed->is_blind() 
-       && m_cdt.triangle(seed).area() != 0)
+       && !m_cdt.triangle(seed).is_degenerate() )
        //to avoid flat triangles outside the domain
     {
       std::stack<Face_handle> faces;
diff --git a/Mesh_2/include/CGAL/Mesh_2/Lloyd_move_2.h b/Mesh_2/include/CGAL/Mesh_2/Lloyd_move_2.h
index 6199445c91c..dadc06875c8 100644
--- a/Mesh_2/include/CGAL/Mesh_2/Lloyd_move_2.h
+++ b/Mesh_2/include/CGAL/Mesh_2/Lloyd_move_2.h
@@ -74,7 +74,7 @@ namespace Mesh_2
 
         // Compute mass
         FT density = density_2d(tri_centroid, sizing_field);
-        FT abs_area = CGAL::abs(tri.area());
+        FT abs_area = CGAL::abs(cdt.geom_traits().compute_area_2_object()(tri[0], tri[1], tri[2]));
         FT mass = abs_area * density;
 
         move = move + mass * Vector_2(p, tri_centroid);
diff --git a/Mesh_2/test/Mesh_2/test_mesh_opti_projection_traits.cpp b/Mesh_2/test/Mesh_2/test_mesh_opti_projection_traits.cpp
new file mode 100644
index 00000000000..5c8b75ed100
--- /dev/null
+++ b/Mesh_2/test/Mesh_2/test_mesh_opti_projection_traits.cpp
@@ -0,0 +1,61 @@
+#define CGAL_MESH_2_OPTIMIZER_VERBOSE
+//#define CGAL_MESH_2_OPTIMIZERS_DEBUG
+//#define CGAL_MESH_2_SIZING_FIELD_USE_BARYCENTRIC_COORDINATES
+
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Constrained_Delaunay_triangulation_2.h>
+#include <CGAL/Delaunay_mesher_2.h>
+#include <CGAL/Delaunay_mesh_face_base_2.h>
+#include <CGAL/Delaunay_mesh_vertex_base_2.h>
+#include <CGAL/Delaunay_mesh_size_criteria_2.h>
+#include <CGAL/Projection_traits_xy_3.h>
+
+#include <CGAL/lloyd_optimize_mesh_2.h>
+
+#include <iostream>
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel Ks;
+typedef CGAL::Projection_traits_xy_3<Ks> K;
+typedef CGAL::Delaunay_mesh_vertex_base_2<K>                Vb;
+typedef CGAL::Delaunay_mesh_face_base_2<K>                  Fb;
+typedef CGAL::Triangulation_data_structure_2<Vb, Fb>        Tds;
+typedef CGAL::Constrained_Delaunay_triangulation_2<K, Tds>  CDT;
+typedef CGAL::Delaunay_mesh_size_criteria_2<CDT>            Criteria;
+typedef CGAL::Delaunay_mesher_2<CDT, Criteria>              Mesher;
+
+typedef CDT::Vertex_handle Vertex_handle;
+typedef CDT::Point Point;
+
+
+int main()
+{
+  CDT cdt;
+
+  Vertex_handle va = cdt.insert(Point(-2,0,1));
+  Vertex_handle vb = cdt.insert(Point(0,-2,1));
+  Vertex_handle vc = cdt.insert(Point(2,0,1));
+  Vertex_handle vd = cdt.insert(Point(0,1,1));
+  cdt.insert(Point(2, 0.6,1));
+
+  cdt.insert_constraint(va, vb);
+  cdt.insert_constraint(vb, vc);
+  cdt.insert_constraint(vc, vd);
+  cdt.insert_constraint(vd, va);
+
+  std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
+
+  std::cout << "Meshing..." << std::endl;
+
+  Mesher mesher(cdt);
+  mesher.set_criteria(Criteria(0.125, 0.05));
+  mesher.refine_mesh();
+  
+  std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
+
+  std::cout << "Run Lloyd optimization...";
+  CGAL::lloyd_optimize_mesh_2(cdt,
+    CGAL::parameters::max_iteration_number = 10);
+  std::cout << " done." << std::endl;
+
+  std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
+}