diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
index 88dc0c830e9..1c23b587093 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
@@ -1697,10 +1697,6 @@ bounded_error_squared_Hausdorff_distance_impl(const TriangleMesh1& tm1,
       CGAL_assertion(sub_triangle_bounds.tm2_lface != boost::graph_traits<TriangleMesh2>::null_face());
       CGAL_assertion(sub_triangle_bounds.tm2_uface != boost::graph_traits<TriangleMesh2>::null_face());
 
-      // Add the subtriangle to the candidate list if it is meaningful
-      if(sub_triangle_bounds.upper < global_bounds.lower)
-        continue;
-
       // The global lower bound is the max of the per-face lower bounds
       if(sub_triangle_bounds.lower > global_bounds.lower)
       {
@@ -1717,16 +1713,13 @@ bounded_error_squared_Hausdorff_distance_impl(const TriangleMesh1& tm1,
       candidate_triangles.emplace(sub_triangles[i], sub_triangle_bounds, triangle_and_bounds.tm1_face);
     }
 
-    // In case all subdividing triangles of the last queue entry are useless
-    if(candidate_triangles.empty())
-      break;
-
     // Update global upper Hausdorff bound after subdivision.
     const Candidate& top_candidate = candidate_triangles.top();
     const FT current_upmost = top_candidate.bounds.upper;
 #ifdef CGAL_HAUSDORFF_DEBUG_PP
-    std::cout << "current upper bound = " << current_upmost << std::endl;
     std::cout << "global_bounds.lower = " << global_bounds.lower << std::endl;
+    std::cout << "global_bounds.upper = " << global_bounds.upper << std::endl;
+    std::cout << "current upper bound = " << current_upmost << std::endl;
 #endif
 
     CGAL_assertion(is_positive(current_upmost));