diff --git a/Surface_sweep_2/include/CGAL/Surface_sweep_2/Surface_sweep_2_impl.h b/Surface_sweep_2/include/CGAL/Surface_sweep_2/Surface_sweep_2_impl.h
index de98db8e9a0..41d96180310 100644
--- a/Surface_sweep_2/include/CGAL/Surface_sweep_2/Surface_sweep_2_impl.h
+++ b/Surface_sweep_2/include/CGAL/Surface_sweep_2/Surface_sweep_2_impl.h
@@ -110,19 +110,28 @@ void Surface_sweep_2<Vis>::_handle_left_curves()
         this->m_currentEvent->push_back_curve_to_right(sc);
       }
       else {
-        this->m_currentEvent->push_back_curve_to_left(sc);
         this->m_currentEvent->set_weak_intersection();
-        this->m_visitor->update_event(this->m_currentEvent, sc);
-        _add_curve_to_right(this->m_currentEvent, sc);
+        auto status_line_it = this->m_status_line_insert_hint;
+        do{
+          this->m_currentEvent->push_back_curve_to_left(sc);
+          this->m_visitor->update_event(this->m_currentEvent, sc);
+          _add_curve_to_right(this->m_currentEvent, sc);
+          ++status_line_it;
+          if (status_line_it==this->m_statusLine.end()) break;
+          if (this->m_statusLineCurveLess(this->m_currentEvent->point(), *status_line_it)!=EQUAL)
+            break;
+          sc = *status_line_it;
+        }
+        while(true); // the loop is only needed in case there are overlapping curve in right curves
       }
 
-      // sc is now on the left
+      // some subcurves have been addded on the left
       CGAL_SS_PRINT_TEXT("Event after update:");
       CGAL_SS_PRINT_EOL();
       CGAL_SS_PRINT_EVENT_INFO(this->m_currentEvent);
       CGAL_SS_PRINT_EOL();
       CGAL_assertion(std::distance(this->m_currentEvent->left_curves_begin(),
-                                   this->m_currentEvent->left_curves_end())==1);
+                                   this->m_currentEvent->left_curves_end())!=0);
     }
     else {
       // The event is not located on any subcurve.