diff --git a/Surface_mesh_topology/examples/Surface_mesh_topology/edgewidth_surface_mesh.cpp b/Surface_mesh_topology/examples/Surface_mesh_topology/edgewidth_surface_mesh.cpp
index c879a61c193..5adae277506 100644
--- a/Surface_mesh_topology/examples/Surface_mesh_topology/edgewidth_surface_mesh.cpp
+++ b/Surface_mesh_topology/examples/Surface_mesh_topology/edgewidth_surface_mesh.cpp
@@ -41,12 +41,12 @@ int main(int argc, char* argv[])
   inp>>sm;
   std::cout<<"File '"<<filename<<"' loaded. Finding edge-width of the mesh..."<<std::endl;
 
-  CGAL::Surface_mesh_topology::Curves_on_surface_topology<Mesh> cst(sm);
+  CGAL::Surface_mesh_topology::Curves_on_surface_topology<Mesh> cst(sm, true);
 
-  Path_on_surface cycle1=cst.compute_edgewidth();
+  Path_on_surface cycle1=cst.compute_edgewidth(true);
 
   CGAL::Surface_mesh_topology::Euclidean_length_weight_functor<Mesh> wf(sm);
-  Path_on_surface cycle2=cst.compute_edgewidth(wf);
+  Path_on_surface cycle2=cst.compute_edgewidth(wf, true);
 
   std::cout<<"Cycle 1 (pink): "; display_cycle_info(sm, cycle1);
   std::cout<<"Cycle 2 (green): "; display_cycle_info(sm, cycle2);
diff --git a/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Edge_weight_functor.h b/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Edge_weight_functor.h
index ff703c18fbf..814e9cec21f 100644
--- a/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Edge_weight_functor.h
+++ b/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Edge_weight_functor.h
@@ -40,9 +40,9 @@ struct Euclidean_length_weight_functor
 
   Weight_t operator() (Dart_const_handle dh) const
   {
-    CGAL::sqrt(CGAL::squared_distance
-               (Get_traits<Mesh>::get_point(m_mesh, dh),
-                Get_traits<Mesh>::get_point(m_mesh, m_map.other_extremity(dh))));
+    return CGAL::sqrt(CGAL::squared_distance
+                      (Get_traits<Mesh>::get_point(m_mesh, dh),
+                       Get_traits<Mesh>::get_point(m_mesh, m_map.other_extremity(dh))));
   }
 
 protected:
diff --git a/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Shortest_noncontractible_cycle.h b/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Shortest_noncontractible_cycle.h
index 284203dd8bf..a2ceab80d9b 100644
--- a/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Shortest_noncontractible_cycle.h
+++ b/Surface_mesh_topology/include/CGAL/Surface_mesh_topology/internal/Shortest_noncontractible_cycle.h
@@ -108,7 +108,7 @@ public:
   // Here amesh is already closed, and have 0-attributes with int.
   // Thus the mesh is not copied.
   Shortest_noncontractible_cycle(Mesh* amesh, size_type perforated_mark,
-                                 bool display_time=false) :
+                                 bool /*display_time*/=false) :
     m_local_map(amesh),
     m_is_perforated(perforated_mark),
     m_cycle(*amesh)
@@ -522,11 +522,11 @@ protected:
     Original_dart_const_handle
         dh_original=Get_original_dart<Self, Copy>::run(this, dh);
     if (cycle.can_be_pushed(dh_original, flip))
-    { cycle.push_back(dh_original, flip); }
+    { cycle.push_back(dh_original, flip, false); }
     else
     {
       CGAL_assertion(cycle.can_be_pushed(dh_original, !flip));
-      cycle.push_back(dh_original, !flip);
+      cycle.push_back(dh_original, !flip, false);
     }
   }
 
@@ -576,6 +576,7 @@ protected:
     // Trace back the path from `b` to root
     for (int ind=min_b-1; ind!=-1; ind=m_trace_index[ind])
     { add_to_cycle(m_spanning_tree[ind], cycle, true); }
+    cycle.update_is_closed();
     CGAL_assertion(cycle.is_closed());
 
     return true;