diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
index 369ed0d0e3c..80be34a152d 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
@@ -48,7 +48,7 @@ namespace internal {
     int n;
     Indentation_level() : n(0) {}
     friend std::ostream& operator<<(std::ostream& os, Indentation_level level) {
-      return os << std::string(2*level.n, ' ');
+      return os << std::setw(2) << level.n << ": " << std::string(2*level.n, ' ');
     }
     Indentation_level& operator++() { ++n; return *this; }
     Indentation_level& operator--() { --n; return *this; }
@@ -754,11 +754,11 @@ insert_constraint(Vertex_handle  vaa, Vertex_handle vbb)
       if (vi != vaa && vi != vbb) {
 #ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
   std::cerr << CGAL::internal::cdt_2_indent_level
-            << "CT_2::insert_constraint stask push [vaa, vi] ( #" << vaa->time_stamp() << "= " << vaa->point()
+            << "CT_2::insert_constraint stack push [vaa, vi] ( #" << vaa->time_stamp() << "= " << vaa->point()
             << " , #" << vi->time_stamp() << "= " << vi->point()
             << " )\n";
   std::cerr << CGAL::internal::cdt_2_indent_level
-            << "CT_2::insert_constraint stask push [vi, vbb] ( #" << vi->time_stamp() << "= " << vi->point()
+            << "CT_2::insert_constraint stack push [vi, vbb] ( #" << vi->time_stamp() << "= " << vi->point()
             << " , #" << vbb->time_stamp() << "= " << vbb->point()
             << " )\n";
 #endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
@@ -768,7 +768,7 @@ insert_constraint(Vertex_handle  vaa, Vertex_handle vbb)
       else{
 #ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
   std::cerr << CGAL::internal::cdt_2_indent_level
-            << "CT_2::insert_constraint stask push [vaa, vbb]( #" << vaa->time_stamp() << "= " << vaa->point()
+            << "CT_2::insert_constraint stack push [vaa, vbb]( #" << vaa->time_stamp() << "= " << vaa->point()
             << " , #" << vbb->time_stamp() << "= " << vbb->point()
             << " )\n";
 #endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h
index 78b66f39e8e..b899fd042b0 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_plus_2.h
@@ -272,6 +272,12 @@ public:
 
   Constraint_id insert_constraint(Vertex_handle va, Vertex_handle vb)
   {
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::insert_constraint( #" << va->time_stamp() << "= " << va->point()
+            << " , #" << vb->time_stamp() << "= " << vb->point()
+            << " )\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
     // protects against inserting a zero length constraint
     if(va == vb){
       return Constraint_id(nullptr);
@@ -854,6 +860,17 @@ insert_subconstraint(Vertex_handle vaa,
   // insert the subconstraint [vaa vbb]
   // it will eventually be splitted into several subconstraints
 {
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::insert_subconstraint( #" << vaa->time_stamp() << "= " << vaa->point()
+            << " , #" << vbb->time_stamp() << "= " << vbb->point()
+            << " )\n";
+  internal::Indentation_level::Exit_guard exit_guard = CGAL::internal::cdt_2_indent_level.open_new_scope();
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::insert_constraint stack push [va, vb] ( #" << vaa->time_stamp() << "= " << vaa->point()
+            << " , #" << vbb->time_stamp() << "= " << vbb->point()
+            << " )\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
   std::stack<std::pair<Vertex_handle, Vertex_handle> > stack;
   stack.push(std::make_pair(vaa,vbb));
 
@@ -861,15 +878,36 @@ insert_subconstraint(Vertex_handle vaa,
     boost::tie(vaa,vbb) = stack.top();
     stack.pop();
     CGAL_triangulation_precondition( vaa != vbb);
-
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+    std::cerr << CGAL::internal::cdt_2_indent_level
+              << "CT_plus_2::insert_subconstraint, stack pop=( #" << vaa->time_stamp() << "= " << vaa->point()
+              << " , #" << vbb->time_stamp() << "= " << vbb->point()
+              << " ) remaining stack size: "
+              << stack.size() << '\n';
+    CGAL_assertion(this->is_valid());
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
     Vertex_handle vi;
 
     Face_handle fr;
     int i;
     if(this->includes_edge(vaa,vbb,vi,fr,i)) {
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+    std::cerr << CGAL::internal::cdt_2_indent_level
+              << "CT_plus_2::insert_subconstraint, the segment ( #" << vaa->time_stamp() << "= " << vaa->point()
+              << " , #" << vbb->time_stamp() << "= " << vbb->point()
+              << " ) is an edge with #"
+              << vi->time_stamp() << "= " << vi->point()
+              << '\n';
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
       this->mark_constraint(fr,i);
       if (vi != vbb)  {
         hierarchy.split_constraint(vaa,vbb,vi);
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::insert_constraint (includes_edge) stack push [vi, vbb] ( #" << vi->time_stamp() << "= " << vi->point()
+            << " , #" << vbb->time_stamp() << "= " << vbb->point()
+            << " )\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
         stack.push(std::make_pair(vi,vbb));
       }
       continue;
@@ -888,10 +926,28 @@ insert_subconstraint(Vertex_handle vaa,
     if ( intersection) {
       if (vi != vaa && vi != vbb) {
         hierarchy.split_constraint(vaa,vbb,vi);
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::insert_constraint stack push [vaa, vi] ( #" << vaa->time_stamp() << "= " << vaa->point()
+            << " , #" << vi->time_stamp() << "= " << vi->point()
+            << " )\n";
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::insert_constraint stack push [vi, vbb] ( #" << vi->time_stamp() << "= " << vi->point()
+            << " , #" << vbb->time_stamp() << "= " << vbb->point()
+            << " )\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
         stack.push(std::make_pair(vaa,vi));
         stack.push(std::make_pair(vi,vbb));
       }
-      else stack.push(std::make_pair(vaa,vbb));
+      else {
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::insert_constraint stack push [vaa, vbb]( #" << vaa->time_stamp() << "= " << vaa->point()
+            << " , #" << vbb->time_stamp() << "= " << vbb->point()
+            << " )\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
+        stack.push(std::make_pair(vaa,vbb));
+      }
 
       continue;
     }
@@ -1026,6 +1082,14 @@ insert(const Point& a, Locate_type lt, Face_handle loc, int li)
   Vertex_handle va = Triangulation::insert(a,lt,loc,li);
   // update the hierarchy
   if (insert_in_constrained_edge) {
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+    std::cerr << CGAL::internal::cdt_2_indent_level
+              << "  CT_plus_2::insert(" << a << ") = #"
+              << va->time_stamp()
+              << "   insert in constrained edge:  #" << v1->time_stamp() << "= " << v1->point()
+              << " , #" << v2->time_stamp() << "= " << v2->point()
+              << std::endl;
+#endif
     hierarchy.split_constraint(v1,v2,va);
   }
   return va;
@@ -1085,6 +1149,14 @@ intersect(Face_handle f, int i,
   const Point& pb = vb->point();
   const Point& pc = vc->point();
   const Point& pd = vd->point();
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::intersect segment ( #" << va->time_stamp() << "= " << va->point()
+            << " , #" << vb->time_stamp() << "= " << vb->point()
+            << " ) with edge ( #"<< vc->time_stamp() << "= " << vc->point()
+            << " , #" << vd->time_stamp() << "= " << vd->point()
+            << " , Exact_intersections_tag)\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
   Point pi;
   Intersection_tag itag = Intersection_tag();
   CGAL_triangulation_assertion_code( bool ok = )
@@ -1092,6 +1164,11 @@ intersect(Face_handle f, int i,
   CGAL_triangulation_assertion(ok);
 
   Vertex_handle vi = insert(pi, Triangulation::EDGE, f, i);
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::intersect, `vi` is ( #" << vi->time_stamp() << "= " << vi->point()
+            << " )\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
   return vi;
 }
 
@@ -1111,6 +1188,14 @@ intersect(Face_handle f, int i,
   const Point& pb = vbb->point();
   const Point& pc = vcc->point();
   const Point& pd = vdd->point();
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::intersect segment ( #" << vaa->time_stamp() << "= " << vaa->point()
+            << " , #" << vbb->time_stamp() << "= " << vbb->point()
+            << " ) with edge ( #"<< vcc->time_stamp() << "= " << vcc->point()
+            << " , #" << vdd->time_stamp() << "= " << vdd->point()
+            << " , Exact_predicates_tag)\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
 
   Point pi; //creator for point is required here
   Intersection_tag itag = Intersection_tag();
@@ -1133,6 +1218,11 @@ intersect(Face_handle f, int i,
     Triangulation::remove_constrained_edge(f, i);
     vi = insert(pi, f);
   }
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "CT_plus_2::intersect, `vi` is ( #" << vi->time_stamp() << "= " << vi->point()
+            << " )\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
 
   // vi == vc or vi == vd may happen even if intersection==true
   // due to approximate construction of the intersection
diff --git a/Triangulation_2/include/CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h b/Triangulation_2/include/CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h
index 168fc2fc4e8..3713469fc55 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2/internal/Polyline_constraint_hierarchy_2.h
@@ -845,6 +845,14 @@ insert_constraint(T va, T vb){
   Vertex_list*  children = new Vertex_list;
   Context_list* fathers;
 
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "C_hierachy.insert_constraint( #"
+              << va->time_stamp()
+              << ", #"
+              << vb->time_stamp()
+              << ")\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
   typename Sc_to_c_map::iterator scit = sc_to_c_map.find(he);
   if(scit == sc_to_c_map.end()){
     fathers = new Context_list;
@@ -874,6 +882,14 @@ insert_constraint_old_API(T va, T vb){
   Vertex_list*  children = new Vertex_list;
   Context_list* fathers;
 
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "C_hierachy.insert_constraint_old_API( #"
+              << va->time_stamp()
+              << ", #"
+              << vb->time_stamp()
+              << ")\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
   typename Sc_to_c_map::iterator scit = sc_to_c_map.find(he);
   if(scit == sc_to_c_map.end()){
     fathers = new Context_list;
@@ -901,6 +917,14 @@ append_constraint(Constraint_id cid, T va, T vb){
   Edge        he = make_edge(va, vb);
   Context_list* fathers;
 
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "C_hierachy.append_constraint( ..., #"
+              << va->time_stamp()
+              << ", #"
+              << vb->time_stamp()
+              << ")\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
   typename Sc_to_c_map::iterator scit = sc_to_c_map.find(he);
   if(scit == sc_to_c_map.end()){
     fathers = new Context_list;
@@ -1012,6 +1036,16 @@ template <class T, class Compare, class Data>
 void
 Polyline_constraint_hierarchy_2<T,Compare,Data>::
 add_Steiner(T va, T vb, T vc){
+#ifdef CGAL_CDT_2_DEBUG_INTERSECTIONS
+  std::cerr << CGAL::internal::cdt_2_indent_level
+            << "C_hierachy.add_Steinter( #"
+              << va->time_stamp()
+              << ", #"
+              << vb->time_stamp()
+              << ", #"
+              << vc->time_stamp()
+              << ")\n";
+#endif // CGAL_CDT_2_DEBUG_INTERSECTIONS
   Context_list* hcl=nullptr;
   if(!get_contexts(va,vb,hcl)) CGAL_triangulation_assertion(false);