diff --git a/AABB_tree/include/CGAL/AABB_traits.h b/AABB_tree/include/CGAL/AABB_traits.h
index 6bcf44a18af..78959df857b 100644
--- a/AABB_tree/include/CGAL/AABB_traits.h
+++ b/AABB_tree/include/CGAL/AABB_traits.h
@@ -414,7 +414,7 @@ public:
           CGAL::SMALLER : CGAL::LARGER;
       }
 
-    CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound) const
+    CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound, Tag_true&) const
       {
           return GeomTraits().do_intersect_3_object()
           (GeomTraits().construct_sphere_3_object()
@@ -422,6 +422,19 @@ public:
           CGAL::SMALLER : CGAL::LARGER;
       }
 
+    CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound, Tag_false&) const
+      {
+          return GeomTraits().do_intersect_3_object()
+          (GeomTraits().construct_sphere_3_object()
+           (p, GeomTraits().compute_squared_distance_3_object()(p, bound)), bb)?
+          CGAL::SMALLER : CGAL::LARGER;
+      }
+
+    CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound) const
+    {
+      return (*this)(p, bb, bound, typename GeomTraits::Has_filtered_predicates_tag());
+    }
+
       template <class Solid>
       CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const FT& sq_distance) const
       {