diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Weights.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Weights.h
index f14051c0b8c..22c308757e1 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Weights.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Weights.h
@@ -307,8 +307,8 @@ public:
     {
       if( is_border(he,pmesh()) ) { continue; }
 
-      CGAL_assertion(CGAL::is_valid_polygon_mesh(pmesh()));
-      CGAL_assertion(CGAL::is_triangle_mesh(pmesh()));
+      CGAL_expensive_assertion(CGAL::is_valid_polygon_mesh(pmesh()));
+      CGAL_expensive_assertion(CGAL::is_triangle_mesh(pmesh()));
       CGAL_assertion( v0 == target(he, pmesh()) );
       vertex_descriptor v1 = source(he, pmesh());
       vertex_descriptor v_op = target(next(he, pmesh()), pmesh());