diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Hole_filling/Triangulate_hole_polyline.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Hole_filling/Triangulate_hole_polyline.h
index e3c16de3575..3b95209a73c 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Hole_filling/Triangulate_hole_polyline.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Hole_filling/Triangulate_hole_polyline.h
@@ -1142,7 +1142,7 @@ public:
     
     triangulate_all(P, Q, WC, std::make_pair(0,n-1), W, lambda);
 
-    if(W.get(0,n-1) == Weight::NOT_VALID()) {
+    if(W.get(0,n-1) == Weight::NOT_VALID() || n <= 2) {
       #ifndef CGAL_TEST_SUITE
       CGAL_warning(!"Returning no output. No possible triangulation is found!");
       #else
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/data/null_edge.polylines.txt b/Polygon_mesh_processing/test/Polygon_mesh_processing/data/null_edge.polylines.txt
new file mode 100644
index 00000000000..5ef80544145
--- /dev/null
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/data/null_edge.polylines.txt
@@ -0,0 +1 @@
+3 -1 -1 0 1 1 0 -1 -1 0
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_hole_polyline_test.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_hole_polyline_test.cpp
index 04cc90402c7..c6998746633 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_hole_polyline_test.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/triangulate_hole_polyline_test.cpp
@@ -223,6 +223,8 @@ void test_should_be_no_output(const char* file_name, bool use_DT) {
 
   test_should_be_no_output("data/collinear.polylines.txt", true);
   test_should_be_no_output("data/collinear.polylines.txt", false);
+  test_should_be_no_output("data/null_edge.polylines.txt", true);
+  test_should_be_no_output("data/null_edge.polylines.txt", false);
   std::cerr << "All Done!" << std::endl;
  }
 
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PMP/Hole_filling_polyline_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/PMP/Hole_filling_polyline_plugin.cpp
index 561dbeb7163..0b1c3a79f5f 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PMP/Hole_filling_polyline_plugin.cpp
+++ b/Polyhedron/demo/Polyhedron/Plugins/PMP/Hole_filling_polyline_plugin.cpp
@@ -114,8 +114,14 @@ public Q_SLOTS:
       print_message(QString("Triangulated in %1 sec.").arg(timer.time()));
 
       if(patch.empty()) {
-        print_message("Warning: generating patch is not successful, please try it without 'Delaunay Triangulation'!");
-        continue;
+        if(use_DT){
+          print_message("Warning: generating patch is not successful, please try it without 'Delaunay Triangulation'!");
+          continue;
+        }
+        else{
+          print_message("Warning: generating patch is not successful, skipping.");
+          continue;
+        }
       }
 
       if(mw->property("is_polyhedron_mode").toBool()){