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 f9bd7e82425..a9ad7c689ed 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
@@ -1733,14 +1733,15 @@ bounded_error_squared_Hausdorff_distance_impl(const TriangleMesh1& tm1,
       std::cout << "Top of the queue is lower than the lowest!" << std::endl;
 #endif
 
+      // This can happen if the actual Hausdorff distance is smaller than sq_initial_bound,
+      // which can happen either if the error bound is really large, or if the initial bound
+      // is non-zero (symmetric Hausdorff distance). In this case, we return 'sq_initial_bound'
+      CGAL_assertion(global_bounds.lower == sq_initial_bound);
+
       global_bounds.upper = global_bounds.lower; // not really needed since lower is returned but doesn't hurt
       global_bounds.upair.first = global_bounds.lpair.first;
       global_bounds.upair.second = global_bounds.lpair.second;
 
-      // Current upmost being equal to the lower is fine, but if it's strictly below, it must
-      // be because we crossed the error bound, or there is some issue...
-      CGAL_assertion(global_bounds.lower == sq_error_bound);
-
       break;
     }