diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_Delaunay_triangulation_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_Delaunay_triangulation_3.h
index 8dc194be783..10be1c44642 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_Delaunay_triangulation_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_Delaunay_triangulation_3.h
@@ -675,14 +675,14 @@ Periodic_3_Delaunay_triangulation_3<Gt,Tds>::find_conflicts( const Point
   // Reset the conflict flag on the boundary.
   for(typename std::vector<Facet>::iterator fit=facets.begin();
   fit != facets.end(); ++fit) {
-    fit->first->neighbor(fit->second)->set_in_conflict_flag(0);
+    fit->first->neighbor(fit->second)->tds_data().clear();
     *bfit++ = *fit;
   }
 
   // Reset the conflict flag in the conflict cells.
   for(typename std::vector<Cell_handle>::iterator ccit=cells.begin();
       ccit != cells.end(); ++ccit) {
-    (*ccit)->set_in_conflict_flag(0);
+    (*ccit)->tds_data().clear();
     *cit++ = *ccit;
   }
 
diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
index ff656df1292..e1f19e68dd7 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
@@ -2075,12 +2075,6 @@ too_long_edges[vit].push_back(temp_inc_cells[i]->vertex(j));
   *
   * c is the current cell, which must be in conflict.
   * tester is the function object that tests if a cell is in conflict.
-  * the cells in conflict are additionally marked by the in_conflict_flag
-  *
-  * in_conflict_flag value :
-  * 0 -> unknown
-  * 1 -> in conflict
-  * 2 -> not in conflict (== on boundary)
   */
 template <class GT, class TDS>
 template <class Conflict_test, class OutputIteratorBoundaryFacets,
@@ -2096,19 +2090,19 @@ find_conflicts(Cell_handle c, const Offset &current_off,
   CGAL_triangulation_precondition( number_of_vertices() != 0 );
   CGAL_triangulation_precondition( tester(c, current_off) );
 
-  c->set_in_conflict_flag(1);
+  c->tds_data().mark_in_conflict();
   
   *it.second++ = c;
 
   for (int i=0; i< 4; ++i) {
     Cell_handle test = c->neighbor(i);
-    if (test->get_in_conflict_flag() == 1) {
+    if (test->tds_data().is_in_conflict()) {
       if (c < test) {
         *it.third++ = Facet(c, i); // Internal facet.
       }
       continue; // test was already in conflict.
     }
-    if (test->get_in_conflict_flag() == 0) {
+    if (!test->tds_data().is_in_conflict()) {
       Offset o_test = current_off + get_neighbor_offset(c, i, test);
       if (tester(test,o_test)) {
         if (c < test)
@@ -2116,7 +2110,7 @@ find_conflicts(Cell_handle c, const Offset &current_off,
         it = find_conflicts(test, o_test, tester, it);
         continue;
       }
-      test->set_in_conflict_flag(2); // test is on the boundary.
+      test->tds_data().mark_on_boundary(); // test is on the boundary.
     }
     *it.first++ = Facet(c, i);
     for (int j = 0 ; j<4 ; j++){
diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_cell_base_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_cell_base_3.h
index 8bd27a92216..422db8b45fb 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_cell_base_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_cell_base_3.h
@@ -52,14 +52,14 @@ public:
   typedef typename TDS::Cell_handle    Cell_handle;
   typedef typename TDS::Vertex         Vertex;
   typedef typename TDS::Cell           Cell;
+  typedef typename TDS::Cell_data      TDS_data;
 
   template <typename TDS2>
   struct Rebind_TDS {
     typedef Periodic_3_triangulation_ds_cell_base_3<TDS2> Other;
   };
 
-  Periodic_3_triangulation_ds_cell_base_3() : _in_conflict_flag(0),
-      _additional_flag(0), off(0) {
+  Periodic_3_triangulation_ds_cell_base_3() : _additional_flag(0), off(0) {
     set_vertices();
     set_neighbors();
   }
@@ -67,7 +67,7 @@ public:
   Periodic_3_triangulation_ds_cell_base_3(
       const Vertex_handle& v0, const Vertex_handle& v1,
       const Vertex_handle& v2, const Vertex_handle& v3) :
-      _in_conflict_flag(0), _additional_flag(0), off(0) {
+      _additional_flag(0), off(0) {
     set_vertices(v0, v1, v2, v3);
     set_neighbors();
   }
@@ -77,7 +77,7 @@ public:
       const Vertex_handle& v2, const Vertex_handle& v3,
       const Cell_handle&   n0, const Cell_handle&   n1,
       const Cell_handle&   n2, const Cell_handle&   n3) :
-      _in_conflict_flag(0), _additional_flag(0), off(0) {
+      _additional_flag(0), off(0) {
     set_vertices(v0, v1, v2, v3);
     set_neighbors(n0, n1, n2, n3);
   }
@@ -249,15 +249,9 @@ public:
   void * for_compact_container() const { return N[0].for_compact_container(); }
   void * & for_compact_container()     { return N[0].for_compact_container(); }
 
-  // Conflict flag access functions.
-  // This should become a property map or something at some point.
-  void set_in_conflict_flag(unsigned char f) {
-    CGAL_triangulation_assertion(f < 4);
-    _in_conflict_flag = f;
-  }
-  unsigned char get_in_conflict_flag() const {
-    return _in_conflict_flag;
-  }
+  // TDS internal data access functions.
+  TDS_data& tds_data() { return _tds_data; }
+  const TDS_data& tds_data() const { return _tds_data; }
 
   // TODO: Get rid of this flag! Used in convert_to_1_cover.
   // Either use the conflict flag or a std::map.
@@ -272,7 +266,7 @@ public:
 private:
   Cell_handle   N[4];
   Vertex_handle V[4];
-  unsigned char _in_conflict_flag:2;
+  TDS_data _tds_data;
   unsigned char _additional_flag:2;
   // 3 respective bits are the offset in x,y and z
   // right to left: bit[0]-bit[2]: vertex(0),