diff --git a/Interpolation/include/CGAL/Voronoi_intersection_2_traits_3.h b/Interpolation/include/CGAL/Voronoi_intersection_2_traits_3.h
index 07a13938bee..e0f214beba8 100644
--- a/Interpolation/include/CGAL/Voronoi_intersection_2_traits_3.h
+++ b/Interpolation/include/CGAL/Voronoi_intersection_2_traits_3.h
@@ -291,6 +291,24 @@ public:
   typedef typename Rep::Less_distance_to_point_3    Less_distance_to_point_2;
   typedef typename Rep::Compute_squared_distance_3  Compute_squared_distance_2;
 
+  struct Compare_xy_2 {
+    Compare_x_2 cx_2;
+    Compare_y_2 cy_2;
+
+    Compare_xy_2(const Compare_x_2& cx_2, const Compare_y_2& cy_2)
+      : cx_2(cx_2), cy_2(cy_2)
+    {}
+
+    Comparison_result operator()(const Point_2& p, const Point_2& q) const
+    {  
+       Comparison_result res = cx_2(p, q);
+       if (res == EQUAL) {
+         return cy_2(p, q);
+       }
+       return res;
+    }
+  };
+
   //instantiations and creation of functors:
   //for the triangulation:
   Orientation_2
@@ -312,6 +330,10 @@ public:
   compare_y_2_object() const
   { return Compare_y_2(normal); }
 
+  Compare_xy_2
+  compare_xy_2_object() const
+  { return Compare_xy_2(compare_x_2_object(), compare_y_2_object()); }
+
   Less_x_2
   less_x_2_object() const
   { return compare_to_less(compare_x_2_object()); }