diff --git a/Surface_sweep_2/include/CGAL/Surface_sweep_2/Default_event_base.h b/Surface_sweep_2/include/CGAL/Surface_sweep_2/Default_event_base.h
index dd8b20ca1b3..0f28b6d9d6d 100644
--- a/Surface_sweep_2/include/CGAL/Surface_sweep_2/Default_event_base.h
+++ b/Surface_sweep_2/include/CGAL/Surface_sweep_2/Default_event_base.h
@@ -172,7 +172,8 @@ public:
     Subcurve_iterator iter = this->right_curves_begin();
     for (Subcurve_iterator end = this->right_curves_end(); iter!=end; ++iter)
     {
-      if (*iter == curve)
+      // TODO refine the condition
+      if ( (*iter)->is_leaf(curve) || curve->is_leaf(*iter) || curve->has_common_leaf(*iter) )
         break;
     }
     CGAL_assertion( iter!=this->right_curves_end() );
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 a356c8e3494..3cd25731b0d 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
@@ -712,7 +712,9 @@ template <typename Vis>
 
       Point_2 left_end = this->m_traits->construct_min_vertex_2_object()(icv);
       // split the x-monotone curve at current event
-      if ( this->m_queueEventLess(left_end, event_for_overlap) == SMALLER)
+      // TODO handle unbounded curves?
+      // TODO: check event_for_overlap is still needed
+      if ( this->m_queueEventLess(left_end, event_for_overlap==NULL ? this->m_currentEvent : event_for_overlap) == SMALLER)
       {
         this->m_traits->split_2_object()(icv,
                                          event_for_overlap->point(),