diff --git a/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3.h b/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3.h
index 47925a89d30..9316280a313 100644
--- a/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3.h
+++ b/Operations_on_polyhedra/include/CGAL/intersection_of_Polyhedra_3.h
@@ -1718,7 +1718,7 @@ class Intersection_of_Polyhedra_3{
       CGAL_assertion(neighbors.find(i)!=neighbors.end());
       neighbors.erase(i);
     }
-    void make_terminal() {degree=45;}
+    void make_terminal() {if (degree==2) degree=45;}
     bool is_terminal()const {return degree!=2;}
     bool empty() const {return neighbors.empty();}
     int top() const {return *neighbors.begin();}
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersection_impl.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersection_impl.h
index 85f4ae30a9b..f4e9abf097b 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersection_impl.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersection_impl.h
@@ -727,7 +727,7 @@ class Intersection_of_triangle_meshes
       CGAL_assertion(neighbors.count(i)!= 0);
       neighbors.erase(i);
     }
-    void make_terminal() {degree=45;}
+    void make_terminal() {if (degree==2) degree=45;}
     bool is_terminal()const {return degree!=2;}
     bool empty() const {return neighbors.empty();}
     Node_id top() const {return *neighbors.begin();}