diff --git a/Nef_3/include/CGAL/Nef_3/SNC_intersection.h b/Nef_3/include/CGAL/Nef_3/SNC_intersection.h
index b80a7faba8d..a0680452b3c 100644
--- a/Nef_3/include/CGAL/Nef_3/SNC_intersection.h
+++ b/Nef_3/include/CGAL/Nef_3/SNC_intersection.h
@@ -183,18 +183,19 @@ class SNC_intersection : public SNC_const_decorator<SNC_structure_> {
 				  Point_3& p) const {
     if(s2.has_on(s1.target())) 
       return false;
-    return (does_intersect_internally(Ray_3(s1.source(), s1.target()), s2, p)
-      && s1.has_on(p));
-    
+    Ray_3 r(s1.source(), s1.target());
+    if(!does_intersect_internally(r, s2, p))
+      return false;
+    Plane_3 pl(s1.target(), r.to_vector());
+    return (pl.oriented_side(p) == CGAL::NEGATIVE);
   }
 
   bool does_intersect_internally( const Ray_3& s1, 
 				  const Segment_3& s2, 
 				  Point_3& p) const {
-    CGAL_NEF_TRACEN("does intersect internally without  LINE3_LINE3_INTERSECTION");
-    if ( s1.is_degenerate() || s2.is_degenerate())
-      // the segment is degenerate so there is not internal intersection 
-      return false;
+    CGAL_NEF_TRACEN("does intersect internally without  LINE3_LINE3_INTERSECTION");    
+    CGAL_assertion(!s1.is_degenerate());
+    CGAL_assertion(!s2.is_degenerate());
     if ( orientation( s1.source(), s1.point(1), s2.source(), s2.target()) 
 	 != COPLANAR)
       // the segments doesn't define a plane
@@ -217,7 +218,14 @@ class SNC_intersection : public SNC_const_decorator<SNC_structure_> {
     // since line(s1) and line(s2) are not parallel they intersects in only
     //   one point 
     CGAL::assign( p ,o);
-    return( s1.has_on(p) && s2.has_on(p));
+    Plane_3 pl(s1.source(), vs1);
+    if(pl.oriented_side(p) != CGAL::POSITIVE)
+      return false;
+    pl = Plane_3(s2.source(), vs2);
+    if(pl.oriented_side(p) != CGAL::POSITIVE)
+      return false;
+    pl = Plane_3(s2.target(), vs2);
+    return (pl.oriented_side(p) == CGAL::NEGATIVE);
   }
     
 #endif // LINE3_LINE3_INTERSECTION
@@ -268,12 +276,8 @@ class SNC_intersection : public SNC_const_decorator<SNC_structure_> {
     CGAL_NEF_TRACEN("-> facet's plane: " << h);
     CGAL_NEF_TRACEN("-> a point on the plane: " << h.point());
     CGAL_NEF_TRACEN("-> ray: " << ray);
-    if( ray.is_degenerate())
-      /* no possible internal intersection */
-      return false;
-    if( h.has_on( ray.source()))
-      /* no possible internal intersection */
-	return false;
+    CGAL_assertion(!ray.is_degenerate());
+    CGAL_assertion(!h.has_on(ray.source()));
     Object o = intersection( h, ray);
     if( !CGAL::assign( p, o))
       return false;
@@ -291,9 +295,7 @@ class SNC_intersection : public SNC_const_decorator<SNC_structure_> {
     CGAL_NEF_TRACEN("-> facet's plane: " << h);
     CGAL_NEF_TRACEN("-> a point on the plane: " << h.point());
     CGAL_NEF_TRACEN("-> ray: " << ray);
-    if( ray.is_degenerate())
-      /* no possible internal intersection */
-      return false;
+    CGAL_assertion(!ray.is_degenerate());
     if( h.has_on( ray.source()))
       /* no possible internal intersection */
 	return false;
@@ -314,9 +316,7 @@ class SNC_intersection : public SNC_const_decorator<SNC_structure_> {
     CGAL_NEF_TRACEN("-> facet's plane: " << h);
     CGAL_NEF_TRACEN("-> a point on the plane: " << h.point());
     CGAL_NEF_TRACEN("-> segment: " << seg);
-    if( seg.is_degenerate())
-      /* no possible internal intersection */
-      return false;
+    CGAL_assertion(!seg.is_degenerate());
     if( h.has_on( seg.source()) || h.has_on(seg.target()))
       /* no possible internal intersection */
       return false;
@@ -344,9 +344,7 @@ class SNC_intersection : public SNC_const_decorator<SNC_structure_> {
     CGAL_NEF_TRACEN("-> facet's plane: " << h);
     CGAL_NEF_TRACEN("-> a point on the plane: " << h.point());
     CGAL_NEF_TRACEN("-> segment: " << seg);
-    if( seg.is_degenerate())
-      /* no possible internal intersection */
-      return false;
+    CGAL_assertion(!seg.is_degenerate());
     if( h.has_on( seg.source()) || h.has_on(seg.target()))
       /* no possible internal intersection */
       return false;