diff --git a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
index 8980c453104..a93004ad293 100644
--- a/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
+++ b/Cartesian_kernel/include/CGAL/Cartesian/function_objects.h
@@ -631,7 +631,6 @@ namespace CartesianKernelFunctors {
     typedef typename K::Point_2   Point_2;
     typedef typename K::Line_2    Line_2;
     typedef typename K::Equal_2   Equal_2;
-    typedef typename K::Less_signed_distance_to_line_2 Less_signed_distance_to_line_2;
 
   public:
     typedef typename K::Comparison_result     result_type;
@@ -641,7 +640,8 @@ namespace CartesianKernelFunctors {
                const Point_2& c, const Point_2& d) const
     {
       CGAL_kernel_precondition_code(Equal_2 equal;)
-          CGAL_kernel_precondition(! equal(a,b));
+      CGAL_kernel_precondition(! equal(a,b));
+
       return cmp_signed_dist_to_lineC2( a.x(), a.y(),
                                         b.x(), b.y(),
                                         c.x(), c.y(),
@@ -651,10 +651,9 @@ namespace CartesianKernelFunctors {
     result_type
     operator()(const Line_2& l, const Point_2& p, const Point_2& q) const
     {
-      Less_signed_distance_to_line_2 less = K().less_signed_distance_to_line_2_object();
-      if (less(l, p, q)) return SMALLER;
-      if (less(l, q, p)) return LARGER;
-      return EQUAL;
+      return cmp_signed_dist_to_directionC2(l.a(), l.b(),
+                                            p.x(), p.y(),
+                                            q.x(), q.y());
     }
   };