diff --git a/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Sphere_3_do_intersect.h b/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Sphere_3_do_intersect.h
index ff1a7ffb4eb..e4d3818043c 100644
--- a/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Sphere_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/Intersections_3/internal/Segment_3_Sphere_3_do_intersect.h
@@ -28,12 +28,33 @@ do_intersect(const typename K::Sphere_3& sp,
              const K& k)
 {
   typedef typename K::RT RT;
-  RT num, den;
+  typedef typename K::Bounded_side Bounded_side;
+
+  typename K::Bounded_side_3 bounded_side = k.bounded_side_3_object();
+  typename K::Compute_squared_radius_3 sq_radius = k.compute_squared_radius_3_object();
+  typename K::Construct_center_3 center = k.construct_center_3_object();
+  typename K::Construct_source_3 source = k.construct_source_3_object();
+  typename K::Construct_target_3 target = k.construct_target_3_object();
+
+  const Bounded_side source_side = bounded_side(sp, source(seg));
+  const Bounded_side target_side = bounded_side(sp, target(seg));
+
+  if(source_side != target_side)
+    return true;
+  else if(source_side == ON_BOUNDED_SIDE) // else if ==> both extremities are on the same side
+    return false;
+  else if(source_side == ON_BOUNDARY)
+    return true;
+
+  CGAL_kernel_assertion(source_side == ON_UNBOUNDED_SIDE && target_side == ON_UNBOUNDED_SIDE);
+
+  // Both out can still be intersecting the sphere
+  RT num, den;
+  CGAL::internal::squared_distance_RT(center(sp), seg, num, den, k);
 
-  CGAL::internal::squared_distance_RT(sp.center(), seg, num, den, k);
   return !(compare_quotients<RT>(num, den,
-                                 Rational_traits<typename K::FT>().numerator(sp.squared_radius()),
-                                 Rational_traits<typename K::FT>().denominator(sp.squared_radius())) == LARGER);
+                                 Rational_traits<typename K::FT>().numerator(sq_radius(sp)),
+                                 Rational_traits<typename K::FT>().denominator(sq_radius(sp))) == LARGER);
 }
 
 template <class K>
diff --git a/Intersections_3/test/Intersections_3/test_intersections_Segment_3.cpp b/Intersections_3/test/Intersections_3/test_intersections_Segment_3.cpp
index 7e56289423e..e8dd7a23868 100644
--- a/Intersections_3/test/Intersections_3/test_intersections_Segment_3.cpp
+++ b/Intersections_3/test/Intersections_3/test_intersections_Segment_3.cpp
@@ -68,16 +68,17 @@ public:
     // see segment_segment.cpp
   }
 
-  // @fixme EPICK
   void S_Sph()
   {
     std::cout << "Segment - Sphere\n";
 
     // No intersection
     check_do_not_intersect(S(p(4,1,9), p(4,6,-1)), Sph(p(9,2,4), 1));
-     check_do_not_intersect(S(p(-2,3,4), p(1,2,-1)), Sph(p(9,2,4), 10000));
+    check_do_not_intersect(S(p(-2,3,4), p(1,2,-1)), Sph(p(9,2,4), 10000));
 
+    check_do_intersect(S(p(0,1,0), p(2,1,0)), Sph(p(1,0,0), 1));
     check_do_intersect(S(p(-2,3,4), p(1,2,-1)), Sph(p(9,2,4), 100));
+    check_do_intersect(S(p(-2,3,4), p(3,2,-5)), Sph(p(9,2,4), 100));
 
     for(int i=0; i<N; ++i)
     {
@@ -92,8 +93,6 @@ public:
       Sph sph(c, sqr);
       if(sph.oriented_side(s0) != sph.oriented_side(s1))
         check_do_intersect(sph, S(s0, s1));
-      else
-        check_do_not_intersect(sph, S(s0, s1));
     }
   }
 
@@ -182,7 +181,7 @@ public:
     std::cout << "3D Segment Intersection tests\n";
 
     S_S();
-//    S_Sph(); // @fixme
+    S_Sph();
     S_Tet();
     S_Tr();
   }