diff --git a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
index 3ce8b3efd61..70e4520ef53 100644
--- a/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
+++ b/Intersections_3/include/CGAL/internal/Intersections_3/Bbox_3_Segment_3_do_intersect.h
@@ -258,13 +258,15 @@ namespace internal {
     CGAL_assertion(dzmax >= 0);
 
     // If t1 > tymax/dymax || tymin/dymin > t2, return false.
-    if( dymax > 0 && dmin > 0 && (dmin*tymax) < (dymax*tmin) ) return false;
-    if( dymin > 0 && dmax > 0 && (dmax*tymin) > (dymin*tmax) ) return false;
+    if( py != qy && px != qx) { // dmin > 0, dymax >0, dmax > 0, dymin > 0
+      if( (dmin*tymax) < (dymax*tmin) ) return false; // TEST TO FILTER
+      if( (dmax*tymin) > (dymin*tmax) ) return false; // TEST TO FILTER
+    }
 
     // If tymin/dymin > t1, set t1 = tymin/dymin.
     if( (px == qx) || // <=> (dmin == 0)
         ( (py != qy) && // <=> (dymin > 0)
-          (dmin*tymin) > (dymin*tmin) ) )
+          (dmin*tymin) > (dymin*tmin) ) )  // TEST TO FILTER
     {
       tmin = tymin;
       dmin = dymin;
@@ -273,7 +275,7 @@ namespace internal {
     // If tymax/dymax < t2, set t2 = tymax/dymax.
     if( (px == qx) || // <=> (dmax > 0)
         ( (py != qy) && // <=> dymax > 0
-          (dmax*tymax) < (dymax*tmax) ) )
+          (dmax*tymax) < (dymax*tmax) ) ) // TEST TO FILTER
     {
       tmax = tymax;
       dmax = dymax;
@@ -285,8 +287,13 @@ namespace internal {
     // CGAL_assertion((dmax == 0) == (px == qx && py == qy));
 
     // If t1 > tzmax || tzmin > t2, return false.
-    if( dmin > 0 && dzmax > 0 && (dmin*tzmax) < (dzmax*tmin) ) return false;
-    if( dmax > 0 && dzmin > 0 && (dmax*tzmin) > (dzmin*tmax) ) return false;
+    if( (px != qx ||
+         py != qy ) &&
+        (pz != qz) ) // dmin > 0, dmax > 0, dzmax > 0, dzmin > 0
+    {
+      if( (dmin*tzmax) < (dzmax*tmin) ) return false; // TEST TO FILTER
+      if( (dmax*tzmin) > (dzmin*tmax) ) return false; // TEST TO FILTER
+    }
     return true;
   }