diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Ray_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Ray_3_do_intersect.h
index e6e125107f0..4659dda8c45 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Ray_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Ray_3_do_intersect.h
@@ -38,11 +38,8 @@ do_intersect(const typename K::Line_3& l,
   if(p0p1s == COLLINEAR)
     return true;
 
-  CGAL::Orientation stp0 = pred(r.source(), r.second_point(), l.point(0));
-  if(stp0 == COLLINEAR)
-    return Ray_3_has_on_collinear_Point_3(r,l.point(0),k);
-
-  return (p0p1s != stp0);
+  typename K::Point_3 lst = l.point(0) + (r.point(1) - r.point(0));
+  return (pred(l.point(0), l.point(1), r.point(0), lst) != CGAL::POSITIVE);
 }
 
 template <class K>
diff --git a/Intersections_3/test/Intersections_3/test_intersections_Line_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_Line_3.cpp
index 6fe55a40654..936e077e018 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_Line_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_Line_3.cpp
@@ -232,6 +232,10 @@ public:
     check_no_intersection(L(p(0,0,0),p(1,0,0)), R(p(3,0,1),p(6,0,1)));
     check_no_intersection(L(p(0,0,0),p(1,0,0)), R(p(0,2,0),p(0,4,0)));
     check_no_intersection(L(p(0,0,0),p(1,0,0)), R(p(6,2,0),p(5,4,0)));
+    check_no_intersection(L(p(0,0,0),p(0,1,0)), R(p(1,-1,0),p(1,0,0)));
+    check_no_intersection(L(p(0,-10,0),p(0,-9,0)), R(p(1,-1,0),p(2,0,0)));
+    check_no_intersection(L(p(0,-10,0),p(0,0,0)), R(p(1,-1,0),p(2,0,0)));
+    check_no_intersection(L(p(0,0,0),p(0,1,0)), R(p(1,-1,0),p(2,0,0)));
 
     // Point intersection
     check_intersection   (L(p(0,0,0),p(1,0,0)), R(p(3,0,0),p(6,4,0)),
diff --git a/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp
index 6a3dd24bcea..1ce4ab53642 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_Ray_3.cpp
@@ -74,6 +74,14 @@ public:
     check_no_intersection  (R(p(0,0,0), p(1,0,0)), R(p(0,1,0), p(0,2,0)));
     check_no_intersection  (R(p(0,0,0), p(1,0,0)), R(p(-1,0,0), p(-1,-1,0)));
 
+    check_no_intersection  (R(p(1,-1,0), p(2,0,0)), R(p(2,-1,0), p(3,0,0)));
+    check_no_intersection  (R(p(1,-1,0), p(2,0,0)), R(p(2,-1,0), p(3,-1,0)));
+    check_no_intersection  (R(p(1,-1,0), p(2,0,0)), R(p(2,-1,0), p(3,-2,0)));
+    check_no_intersection  (R(p(0,0,0), p(0,1,0)), R(p(0,-1,0), p(1,-1,0)));
+    check_no_intersection  (R(p(0,0,0), p(0,1,0)), R(p(-1,-3,0),p(2,0,0)));
+    check_no_intersection  (R(p(0,0,0), p(0,1,0)), R(p(-2,-4,0),p(-1,-3,0)));
+    check_no_intersection  (R(p(0,0,0), p(0,1,0)), R(p(1,-1,0), p(2,0,0)));
+
     // Point
     check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(0,0,0), p(-1,0,0)),
                             p(0,0,0));
@@ -88,6 +96,10 @@ public:
     check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(1,-2,0), p(1,-1,0)),
                             p(1,0,0));
 
+    check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(1,-2,0), p(1,-1,0)),
+                            p(1,0,0));
+
+
     // Segment
     check_intersection     (R(p(0,0,0), p(1,0,0)), R(p(2,0,0), p(-3,0,0)),
                             S(p(0,0,0), p(2,0,0)), false);