diff --git a/AABB_tree/test/AABB_tree/AABB_test_util.h b/AABB_tree/test/AABB_tree/AABB_test_util.h
index aab0bd348d7..d342d0f1472 100644
--- a/AABB_tree/test/AABB_tree/AABB_test_util.h
+++ b/AABB_tree/test/AABB_tree/AABB_test_util.h
@@ -748,7 +748,7 @@ private:
       FT dist_naive = CGAL::squared_distance(query, point_naive);
       FT dist_tree = CGAL::squared_distance(query, point_tree);
 
-      const FT epsilon = (FT)1e-12;
+      const FT epsilon (1e-8);
       assert( (dist_naive - dist_tree) <= epsilon );
       assert( (dist_naive - dist_tree) >= (-1. * epsilon) );
     }
@@ -783,9 +783,9 @@ private:
         FT dist_naive = CGAL::squared_distance(query, point_naive.first);
         FT dist_tree = CGAL::squared_distance(query, point_tree.first);
 
-        const FT epsilon = (FT)1e-6;
-        assert( (dist_naive - dist_tree) <= (epsilon * dist_tree) );
-        assert( (dist_naive - dist_tree) >= (-1 * epsilon * dist_tree) );
+        const FT epsilon (1e-8);
+        assert( (dist_naive - dist_tree) <= epsilon );
+        assert( (dist_naive - dist_tree) >= (-1. * epsilon) );
       }
     }