diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h
index a3d85e06bd1..415a6641d4e 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/self_intersections.h
@@ -244,7 +244,10 @@ self_intersections( const FaceRange& face_range,
  * @tparam NamedParameters a sequence of \ref pmp_namedparameters "Named Parameters"
  *
  * @param tmesh the triangulated surface mesh to be checked
- * @param out output iterator to be filled with all pairs of non-adjacent faces that intersect
+ * @param out output iterator to be filled with all pairs of non-adjacent faces that intersect.
+              In case `tmesh` contains some degenerate faces, for each degenerate face `f` a pair `(f,f)`
+              will be put in `out` before any other self intersection between non-degenerate faces.
+              These are the only pairs where degenerate faces will be reported.
  * @param np optional sequence of \ref pmp_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
@@ -343,10 +346,15 @@ self_intersections( const FaceRange& face_range,
 
   BOOST_FOREACH(face_descriptor f, face_range)
   {
-    boxes.push_back(Box( get(vpmap, target(halfedge(f,tmesh),tmesh)).bbox()
-      + get(vpmap, target(next(halfedge(f, tmesh), tmesh), tmesh)).bbox()
-      + get(vpmap, target(next(next(halfedge(f, tmesh), tmesh), tmesh), tmesh)).bbox(),
-    f));
+    typename boost::property_traits<VertexPointMap>::reference
+      p = get(vpmap, target(halfedge(f,tmesh),tmesh)),
+      q = get(vpmap, target(next(halfedge(f, tmesh), tmesh), tmesh)),
+      r = get(vpmap, target(next(next(halfedge(f, tmesh), tmesh), tmesh), tmesh));
+
+    if ( collinear(p, q, r) )
+      *out++= std::make_pair(f,f);
+    else
+      boxes.push_back(Box(p.bbox() + q.bbox() + r.bbox(), f));
   }
   // generate box pointers
   std::vector<const Box*> box_ptr;
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/self_intersection_surface_mesh_test.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/self_intersection_surface_mesh_test.cpp
index 9431c547a43..3addd6c9323 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/self_intersection_surface_mesh_test.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/self_intersection_surface_mesh_test.cpp
@@ -115,5 +115,21 @@ int main(int argc, char** argv)
   std::cout << "Third test (Epec):" << std::endl;
   r += test_self_intersections<Epec>(filename, expected);
 
+  // Fourth test ----------------------------------------------------------------
+  expected = true;
+  filename = (argc > 7) ? argv[7] : "data_degeneracies/degtri_single.off";
+  if(argc > 7) {
+    assert(argc > 8);
+    std::stringstream ss(argv[8]);
+    ss >> std::boolalpha >> expected;
+    assert(!ss.fail());
+  }
+
+  std::cout << "Fourth test (Epic):" << std::endl;
+  r += test_self_intersections<Epic>(filename, expected);
+
+  std::cout << "Fourth test (Epec):" << std::endl;
+  r += test_self_intersections<Epec>(filename, expected);
+
   return r;
 }