diff --git a/Packages/Triangulation_3/include/CGAL/Triangulation_ds_iterators_3.h b/Packages/Triangulation_3/include/CGAL/Triangulation_ds_iterators_3.h
index dc774852e20..3c21f81c75d 100644
--- a/Packages/Triangulation_3/include/CGAL/Triangulation_ds_iterators_3.h
+++ b/Packages/Triangulation_3/include/CGAL/Triangulation_ds_iterators_3.h
@@ -554,6 +554,9 @@ public:
 	    notfound = false;
 	  }
 	}
+	else {
+	  b=0; e=1;
+	}
       } while ( (pos != _tds->past_end_cell()) &&
 		notfound );
       break;
@@ -604,12 +607,20 @@ public:
 	    e--;
 	  }
 	}
-	Cell_circulator ccir = _tds->incident_cells(CGAL_make_triple(pos,b,e));
-	while ( &(*ccir) > pos ) {
-	  --ccir;
+	if (pos != _tds->past_end_cell()) {
+	  Cell_circulator ccir = _tds->incident_cells(CGAL_make_triple(pos,b,e));
+// 	while ( &(*ccir) > pos ) {
+// 	  --ccir;
+// 	}
+	  do {
+	    ++ccir;
+	  } while ( &(*ccir) > pos );
+	  if ( &(*ccir) == pos ) {// pos is the cell with minimum pointer
+	    notfound = false;
+	  }
 	}
-	if ( &(*ccir) == pos ) {// pos is the cell with minimum pointer
-	  notfound = false;
+	else {
+	  b=0; e=1;
 	}
       } while ( (pos != _tds->past_end_cell()) &&
 		notfound );
diff --git a/Packages/Triangulation_3/include/CGAL/Triangulation_iterators_3.h b/Packages/Triangulation_3/include/CGAL/Triangulation_iterators_3.h
index 8e8b6d6f063..f512180b28c 100644
--- a/Packages/Triangulation_3/include/CGAL/Triangulation_iterators_3.h
+++ b/Packages/Triangulation_3/include/CGAL/Triangulation_iterators_3.h
@@ -338,7 +338,8 @@ public:
   }
         
   CGAL_Triangulation_edge_iterator_3(CGAL_Triangulation_3<Gt,Tds> *tr)
-    : _ib( &(tr->_tds), 1), _tr(tr)
+    : _ib( &(tr->_tds), 1), _tr(tr), _inf(true)
+    // _inf is initialized but should never be used
   { }
        
   CGAL_Triangulation_edge_iterator_3(const Edge_iterator & ei)
@@ -357,7 +358,14 @@ public:
   bool
   operator==(const Edge_iterator & ei) const
   {
-    return ( _ib == ei._ib);
+    if ( _tr != ei._tr ) 
+      return false;
+
+    if ( ( _ib == _tr->_tds.edges_end() ) 
+	 || ( ei._ib == _tr->_tds.edges_end() ) ) 
+      return ( _ib == ei._ib );
+
+    return ( ( _ib == ei._ib ) && ( _inf == ei._inf ) );
   }
 
   bool
@@ -458,6 +466,7 @@ public:
         
   CGAL_Triangulation_facet_iterator_3(CGAL_Triangulation_3<Gt,Tds> *tr)
     : _ib( &(tr->_tds), 1), _tr(tr), _inf(true)
+  // _inf is initialized but should never be used
   { }
        
   CGAL_Triangulation_facet_iterator_3(const Facet_iterator & fi)
@@ -476,7 +485,14 @@ public:
   bool
   operator==(const Facet_iterator & fi) const
   {
-    return ( _ib == fi._ib);
+    if ( _tr != fi._tr ) 
+      return false;
+
+    if ( ( _ib == _tr->_tds.facets_end() ) 
+	 || ( fi._ib == _tr->_tds.facets_end() ) ) 
+      return ( _ib == fi._ib );
+
+    return ( ( _ib == fi._ib ) && ( _inf == fi._inf ) );
   }
 
   bool
@@ -509,7 +525,7 @@ public:
     else{
       do {
 	--_ib;
-      } while ( ( _ib != _tr->_tds.edges_end() )
+      } while ( ( _ib != _tr->_tds.facets_end() )
 		&& _tr->is_infinite(make_pair(Cell_handle( (Cell *) (*_ib).first), (*_ib).second )) );
     }
     return *this;