diff --git a/Combinatorial_map/include/CGAL/Cell_attribute.h b/Combinatorial_map/include/CGAL/Cell_attribute.h
index 3b239c5f1f9..db0fe4d3917 100644
--- a/Combinatorial_map/include/CGAL/Cell_attribute.h
+++ b/Combinatorial_map/include/CGAL/Cell_attribute.h
@@ -197,8 +197,8 @@ namespace CGAL {
 
     void * for_compact_container() const
     { return vp; }
-    void * & for_compact_container()
-    { return vp; }
+    void for_compact_container(void *p)
+    { vp = p; }
 
   private:
     /// Reference counting: the number of darts linked to this cell.
@@ -310,8 +310,8 @@ namespace CGAL {
 
     void * for_compact_container() const
     { return mdart.for_compact_container(); }
-    void * & for_compact_container()
-    { return mdart.for_compact_container(); }
+    void for_compact_container(void *p)
+    { mdart.for_compact_container(p); }
 
   private:
     /// The dart handle associated with the cell.
diff --git a/Combinatorial_map/include/CGAL/Dart.h b/Combinatorial_map/include/CGAL/Dart.h
index 04d2044c481..2b13b9d7911 100644
--- a/Combinatorial_map/include/CGAL/Dart.h
+++ b/Combinatorial_map/include/CGAL/Dart.h
@@ -105,8 +105,8 @@ namespace CGAL {
 
     void * for_compact_container() const
     { return mf[0].for_compact_container(); }
-    void * & for_compact_container()
-    { return mf[0].for_compact_container(); }
+    void for_compact_container(void *p)
+    { mf[0].for_compact_container(p); }
 
     Dart_handle get_f(unsigned int i) const
     {
diff --git a/Convex_hull_d/include/CGAL/Regular_complex_d.h b/Convex_hull_d/include/CGAL/Regular_complex_d.h
index c0365871c2b..ee50aefc331 100644
--- a/Convex_hull_d/include/CGAL/Regular_complex_d.h
+++ b/Convex_hull_d/include/CGAL/Regular_complex_d.h
@@ -87,7 +87,7 @@ public:
 
   void* pp;
   void*   for_compact_container() const { return pp; }
-  void* & for_compact_container()       { return pp; }
+  void for_compact_container(void *p) { pp = p; }
 
 #ifdef CGAL_USE_LEDA
   LEDA_MEMORY(RC_vertex_d)
@@ -153,7 +153,7 @@ public:
 
   void* pp;
   void*   for_compact_container() const { return pp; }
-  void* & for_compact_container()       { return pp; }
+  void for_compact_container(void *p) { pp = p; }
 
   #if 0
   struct Point_const_iterator {
diff --git a/Interval_skip_list/include/CGAL/Interval_skip_list.h b/Interval_skip_list/include/CGAL/Interval_skip_list.h
index 172e48ebf3f..1c13f5d5cde 100644
--- a/Interval_skip_list/include/CGAL/Interval_skip_list.h
+++ b/Interval_skip_list/include/CGAL/Interval_skip_list.h
@@ -115,7 +115,7 @@ class Interval_for_container : public Interval_
       {}
       
       void *   for_compact_container() const { return p; }
-      void * & for_compact_container()       { return p; }
+      void for_compact_container(void *ptr) { p = ptr; }
     };
 
 
@@ -457,7 +457,7 @@ class Interval_for_container : public Interval_
   public:
 #ifdef CGAL_ISL_USE_CCC
     void *   for_compact_container() const { return p; }
-    void * & for_compact_container()       { return p; }
+    void for_compact_container(void *ptr) { p = ptr; }
 #endif
 
     bool operator==(const IntervalListElt& e)
diff --git a/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h b/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h
index ae091b60be3..cea2e2405ba 100644
--- a/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h
+++ b/Mesh_3/include/CGAL/Compact_mesh_cell_base_3.h
@@ -491,7 +491,7 @@ public:
 
   // For use by Compact_container.
   void * for_compact_container() const { return N[0].for_compact_container(); }
-  void * & for_compact_container()     { return N[0].for_compact_container(); }
+  void for_compact_container(void *p) { N[0].for_compact_container(p); }
 
   // TDS internal data access functions.
         TDS_data& tds_data()       { return _tds_data; }
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 f8f32f0e820..e69b2fe8dba 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
@@ -233,7 +233,7 @@ public:
 
   // For use by Compact_container.
   void * for_compact_container() const { return N[0].for_compact_container(); }
-  void * & for_compact_container()     { return N[0].for_compact_container(); }
+  void for_compact_container(void *p) { N[0].for_compact_container(p); }
 
   // TDS internal data access functions.
   TDS_data& tds_data() { return _tds_data; }
diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_vertex_base_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_vertex_base_3.h
index 539c3278bf3..e264e523063 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_vertex_base_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_ds_vertex_base_3.h
@@ -80,8 +80,8 @@ public:
   // For use by the Compact_container.
   void *   for_compact_container() const
   { return _c.for_compact_container(); }
-  void * & for_compact_container()
-  { return _c.for_compact_container(); }
+  void for_compact_container(void *p)
+  { _c.for_compact_container(p); }
 
 private:
   Cell_handle _c;
diff --git a/STL_Extension/benchmark/compact_container_benchmark/cc_benchmark.cpp b/STL_Extension/benchmark/compact_container_benchmark/cc_benchmark.cpp
index 8daa0bcf94e..3158f09b096 100644
--- a/STL_Extension/benchmark/compact_container_benchmark/cc_benchmark.cpp
+++ b/STL_Extension/benchmark/compact_container_benchmark/cc_benchmark.cpp
@@ -26,7 +26,7 @@ struct Truc
 {
   Truc(int v = 0) : value(v), /*value2(v), */p(NULL) {}
   void *   for_compact_container() const { return p; }
-  void * & for_compact_container()       { return p; }
+  void for_compact_container(void *ptr) { p = ptr; }
 
   int value;
   int value2;
diff --git a/STL_Extension/doc/STL_Extension/CGAL/Compact_container.h b/STL_Extension/doc/STL_Extension/CGAL/Compact_container.h
index a4d4d902bb8..b29bdf8887c 100644
--- a/STL_Extension/doc/STL_Extension/CGAL/Compact_container.h
+++ b/STL_Extension/doc/STL_Extension/CGAL/Compact_container.h
@@ -30,10 +30,9 @@ Returns the pointer necessary for `Compact_container_traits<T>`.
 void * for_compact_container() const; 
 
 /*!
-Returns a reference to the pointer necessary for 
-`Compact_container_traits<T>`. 
+Sets the pointer necessary for `Compact_container_traits<T>` to `p`.
 */ 
-void * & for_compact_container(); 
+void for_compact_container(void* p);
 
 /// @} 
 
@@ -796,7 +795,7 @@ types `T` to make them usable with the default `Compact_container_traits`.
 
 `void * t.for_compact_container() const;` 
 
-`void *& t.for_compact_container();`. 
+`void t.for_compact_container(void *);`. 
 
 
 */
@@ -820,11 +819,11 @@ static void * pointer(const T &t);
 /// \name Operations 
 /// @{ 
 /*!
-Returns a reference to the pointer held by `t`. 
-The template version defines this function as: `return t.for_compact_container();` 
+Sets the pointer held by `t` to `p`. 
+The template version defines this function as: `t.for_compact_container(p);` 
 
 */ 
-static void * & pointer(T &t); 
+  static void set_pointer(T &t, void* p); 
 
 
 
diff --git a/STL_Extension/doc/STL_Extension/CGAL/Concurrent_compact_container.h b/STL_Extension/doc/STL_Extension/CGAL/Concurrent_compact_container.h
index 74c2ce4d5d7..8f55b19bb7f 100644
--- a/STL_Extension/doc/STL_Extension/CGAL/Concurrent_compact_container.h
+++ b/STL_Extension/doc/STL_Extension/CGAL/Concurrent_compact_container.h
@@ -22,7 +22,7 @@ types `T` to make them usable with the default `Concurrent_compact_container`.
 
 `T` is any type providing the following member functions: 
 `void * t.for_compact_container() const;` 
-`void *& t.for_compact_container();`.
+`void t.for_compact_container(void *);`.
 */
 template< typename T >
 struct Concurrent_compact_container_traits {
@@ -40,11 +40,11 @@ struct Concurrent_compact_container_traits {
 /// \name Operations 
 /// @{ 
   /*! 
-  Returns a reference to the pointer held by `t`. 
-  The template version defines this function as: `return t.for_compact_container();` 
+  Sets the pointer held by `t` to `p`.
+  The template version defines this function as: `t.for_compact_container(p);`
 
   */ 
-  static void * & pointer(T &t); 
+  static void set_pointer(T &t, void* p);
 
 /// @} 
 
diff --git a/STL_Extension/include/CGAL/Compact_container.h b/STL_Extension/include/CGAL/Compact_container.h
index f6946fc2758..2781d5befe9 100644
--- a/STL_Extension/include/CGAL/Compact_container.h
+++ b/STL_Extension/include/CGAL/Compact_container.h
@@ -149,15 +149,15 @@ public:
   Compact_container_base()
   : p(nullptr) {}
   void *   for_compact_container() const { return p; }
-  void * & for_compact_container()       { return p; }
+  void for_compact_container(void* ptr)  { p = ptr; }
 };
 
 // The traits class describes the way to access the pointer.
 // It can be specialized.
 template < class T >
 struct Compact_container_traits {
-  static void *   pointer(const T &t) { return t.for_compact_container(); }
-  static void * & pointer(T &t)       { return t.for_compact_container(); }
+  static void *   pointer(const T &t)    { return t.for_compact_container(); }
+  static void set_pointer(T &t, void* p) { t.for_compact_container(p); }
 };
 
 namespace internal {
@@ -645,8 +645,8 @@ private:
     // This out of range compare is always true and causes lots of
     // unnecessary warnings.
     // CGAL_precondition(0 <= t && t < 4);
-    Traits::pointer(*ptr) = reinterpret_cast<void *>
-      (reinterpret_cast<std::ptrdiff_t>(clean_pointer((char *) p)) + (int) t);
+    Traits::set_pointer(*ptr, reinterpret_cast<void *>
+      (reinterpret_cast<std::ptrdiff_t>(clean_pointer((char *) p)) + (int) t));
   }
 
 public:
@@ -872,7 +872,7 @@ namespace internal {
       : ts(0)
 #endif
     {
-      m_ptr.p = nullptr;
+      m_ptr = nullptr;
     }
 
     CC_iterator (const CC_iterator &it)
@@ -880,7 +880,7 @@ namespace internal {
       : ts(Time_stamper::time_stamp(it.operator->()))
 #endif
     {
-      m_ptr.p = it.operator->();
+      m_ptr = it.operator->();
     }
 
     // Converting constructor from mutable to constant iterator
@@ -892,7 +892,7 @@ namespace internal {
         : ts(Time_stamper::time_stamp(const_it.operator->()))
 #endif
     {
-      m_ptr.p = const_it.operator->();
+      m_ptr = const_it.operator->();
     }
 
     // Assignment operator from mutable to constant iterator
@@ -901,7 +901,7 @@ namespace internal {
                 typename std::enable_if<(!OtherConst && Const), DSC>::type,
                 OtherConst> &const_it)
     {
-      m_ptr.p = const_it.operator->();
+      m_ptr = const_it.operator->();
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
       ts = Time_stamper::time_stamp(const_it.operator->());
 #endif
@@ -920,7 +920,7 @@ namespace internal {
 #endif
     {
       CGAL_assertion (n == nullptr);
-      m_ptr.p = nullptr;
+      m_ptr = nullptr;
     }
 
   private:
@@ -929,10 +929,7 @@ namespace internal {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
     std::size_t ts;
 #endif
-    union {
-      pointer      p;
-      void        *vp;
-    } m_ptr;
+    pointer m_ptr;
 
     // Only Compact_container and Concurrent_compact_container should
     // access these constructors.
@@ -948,16 +945,16 @@ namespace internal {
       : ts(0)
 #endif
     {
-      m_ptr.p = ptr;
-      if (m_ptr.p == nullptr) // empty container.
+      m_ptr = ptr;
+      if (m_ptr == nullptr) // empty container.
         return;
 
-      ++(m_ptr.p); // if not empty, p = start
-      if (DSC::type(m_ptr.p) == DSC::FREE)
+      ++(m_ptr); // if not empty, p = start
+      if (DSC::type(m_ptr) == DSC::FREE)
         increment();
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
       else
-        ts = Time_stamper::time_stamp(m_ptr.p);
+        ts = Time_stamper::time_stamp(m_ptr);
 #endif // CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
     }
 
@@ -967,10 +964,10 @@ namespace internal {
       : ts(0)
 #endif
     {
-      m_ptr.p = ptr;
+      m_ptr = ptr;
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
       if(ptr != nullptr){
-        ts = Time_stamper::time_stamp(m_ptr.p);
+        ts = Time_stamper::time_stamp(m_ptr);
       }
 #endif // end CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
     }
@@ -979,49 +976,49 @@ namespace internal {
     void increment()
     {
       // It's either pointing to end(), or valid.
-      CGAL_assertion_msg(m_ptr.p != nullptr,
+      CGAL_assertion_msg(m_ptr != nullptr,
          "Incrementing a singular iterator or an empty container iterator ?");
-      CGAL_assertion_msg(DSC::type(m_ptr.p) != DSC::START_END,
+      CGAL_assertion_msg(DSC::type(m_ptr) != DSC::START_END,
          "Incrementing end() ?");
 
       // If it's not end(), then it's valid, we can do ++.
       do {
-        ++(m_ptr.p);
-        if (DSC::type(m_ptr.p) == DSC::USED ||
-            DSC::type(m_ptr.p) == DSC::START_END)
+        ++(m_ptr);
+        if (DSC::type(m_ptr) == DSC::USED ||
+            DSC::type(m_ptr) == DSC::START_END)
         {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
-          ts = Time_stamper::time_stamp(m_ptr.p);
+          ts = Time_stamper::time_stamp(m_ptr);
 #endif
           return;
         }
-        if (DSC::type(m_ptr.p) == DSC::BLOCK_BOUNDARY)
-          m_ptr.p = DSC::clean_pointee(m_ptr.p);
+        if (DSC::type(m_ptr) == DSC::BLOCK_BOUNDARY)
+          m_ptr = DSC::clean_pointee(m_ptr);
       } while (true);
     }
 
     void decrement()
     {
       // It's either pointing to end(), or valid.
-      CGAL_assertion_msg(m_ptr.p != nullptr,
+      CGAL_assertion_msg(m_ptr != nullptr,
          "Decrementing a singular iterator or an empty container iterator ?");
-      CGAL_assertion_msg(DSC::type(m_ptr.p - 1) != DSC::START_END,
+      CGAL_assertion_msg(DSC::type(m_ptr - 1) != DSC::START_END,
          "Decrementing begin() ?");
 
       // If it's not begin(), then it's valid, we can do --.
       do {
-        --m_ptr.p;
-        if (DSC::type(m_ptr.p) == DSC::USED ||
-            DSC::type(m_ptr.p) == DSC::START_END)
+        --m_ptr;
+        if (DSC::type(m_ptr) == DSC::USED ||
+            DSC::type(m_ptr) == DSC::START_END)
         {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
-          ts = Time_stamper::time_stamp(m_ptr.p);
+          ts = Time_stamper::time_stamp(m_ptr);
 #endif
           return;
         }
 
-        if (DSC::type(m_ptr.p) == DSC::BLOCK_BOUNDARY)
-          m_ptr.p = DSC::clean_pointee(m_ptr.p);
+        if (DSC::type(m_ptr) == DSC::BLOCK_BOUNDARY)
+          m_ptr = DSC::clean_pointee(m_ptr);
       } while (true);
     }
 
@@ -1029,9 +1026,9 @@ namespace internal {
 
     Self & operator++()
     {
-      CGAL_assertion_msg(m_ptr.p != nullptr,
+      CGAL_assertion_msg(m_ptr != nullptr,
          "Incrementing a singular iterator or an empty container iterator ?");
-      /* CGAL_assertion_msg(DSC::type(m_ptr.p) == DSC::USED,
+      /* CGAL_assertion_msg(DSC::type(m_ptr) == DSC::USED,
          "Incrementing an invalid iterator."); */
       increment();
       return *this;
@@ -1039,10 +1036,10 @@ namespace internal {
 
     Self & operator--()
     {
-      CGAL_assertion_msg(m_ptr.p != nullptr,
+      CGAL_assertion_msg(m_ptr != nullptr,
          "Decrementing a singular iterator or an empty container iterator ?");
-      /*CGAL_assertion_msg(DSC::type(m_ptr.p) == DSC::USED
-                      || DSC::type(m_ptr.p) == DSC::START_END,
+      /*CGAL_assertion_msg(DSC::type(m_ptr) == DSC::USED
+                      || DSC::type(m_ptr) == DSC::START_END,
                       "Decrementing an invalid iterator.");*/
       decrement();
       return *this;
@@ -1054,13 +1051,13 @@ namespace internal {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
     bool is_time_stamp_valid() const
     {
-      return (ts == 0) || (ts == Time_stamper::time_stamp(m_ptr.p));
+      return (ts == 0) || (ts == Time_stamper::time_stamp(m_ptr));
     }
 #endif // CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
 
-    reference operator*() const { return *(m_ptr.p); }
+    reference operator*() const { return *(m_ptr); }
 
-    pointer   operator->() const { return (m_ptr.p); }
+    pointer   operator->() const { return (m_ptr); }
 
     // For std::less...
     bool operator<(const CC_iterator& other) const
@@ -1068,7 +1065,7 @@ namespace internal {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
       assert( is_time_stamp_valid() );
 #endif
-      return Time_stamper::less(m_ptr.p, other.m_ptr.p);
+      return Time_stamper::less(m_ptr, other.m_ptr);
     }
 
     bool operator>(const CC_iterator& other) const
@@ -1076,7 +1073,7 @@ namespace internal {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
       assert( is_time_stamp_valid() );
 #endif
-      return Time_stamper::less(other.m_ptr.p, m_ptr.p);
+      return Time_stamper::less(other.m_ptr, m_ptr);
     }
 
     bool operator<=(const CC_iterator& other) const
@@ -1084,7 +1081,7 @@ namespace internal {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
       assert( is_time_stamp_valid() );
 #endif
-      return Time_stamper::less(m_ptr.p, other.m_ptr.p)
+      return Time_stamper::less(m_ptr, other.m_ptr)
           || (*this == other);
     }
 
@@ -1093,13 +1090,13 @@ namespace internal {
 #ifdef CGAL_COMPACT_CONTAINER_DEBUG_TIME_STAMP
       assert( is_time_stamp_valid() );
 #endif
-      return Time_stamper::less(other.m_ptr.p, m_ptr.p)
+      return Time_stamper::less(other.m_ptr, m_ptr)
           || (*this == other);
     }
 
     // Can itself be used for bit-squatting.
-    void *   for_compact_container() const { return (m_ptr.vp); }
-    void * & for_compact_container()       { return (m_ptr.vp); }
+    void * for_compact_container() const { return m_ptr; }
+    void for_compact_container(void* p) { m_ptr = static_cast<pointer>(p); }
   };
 
   template < class DSC, bool Const1, bool Const2 >
diff --git a/STL_Extension/include/CGAL/Concurrent_compact_container.h b/STL_Extension/include/CGAL/Concurrent_compact_container.h
index e968312c453..4d644e547b8 100644
--- a/STL_Extension/include/CGAL/Concurrent_compact_container.h
+++ b/STL_Extension/include/CGAL/Concurrent_compact_container.h
@@ -66,7 +66,7 @@ template<typename T> class has_##X {                                          \
 template < class T >
 struct Concurrent_compact_container_traits {
   static void *   pointer(const T &t) { return t.for_compact_container(); }
-  static void * & pointer(T &t)       { return t.for_compact_container(); }
+  static void set_pointer(T &t, void* p) { t.for_compact_container(p); }
 };
 
 namespace CCC_internal {
@@ -613,8 +613,8 @@ private:
     // This out of range compare is always true and causes lots of
     // unnecessary warnings.
     // CGAL_precondition(0 <= t && t < 4);
-    Traits::pointer(*ptr) = reinterpret_cast<void *>
-      (reinterpret_cast<std::ptrdiff_t>(clean_pointer((char *) p)) + (int) t);
+    Traits::set_pointer(*ptr, reinterpret_cast<void *>
+      (reinterpret_cast<std::ptrdiff_t>(clean_pointer((char *) p)) + (int) t));
   }
 
   typedef tbb::queuing_mutex Mutex;
diff --git a/STL_Extension/test/STL_Extension/test_Compact_container.cpp b/STL_Extension/test/STL_Extension/test_Compact_container.cpp
index 3d370105a6a..e84d79fecfc 100644
--- a/STL_Extension/test/STL_Extension/test_Compact_container.cpp
+++ b/STL_Extension/test/STL_Extension/test_Compact_container.cpp
@@ -72,7 +72,7 @@ public:
   bool operator< (const Node_2 &n) const { return rnd <  n.rnd; }
 
   void *   for_compact_container() const { return p_cc; }
-  void * & for_compact_container()       { return p_cc; }
+  void for_compact_container(void *p)       { p_cc = p; }
 };
 
 template < class Cont >
diff --git a/STL_Extension/test/STL_Extension/test_Compact_container_is_used.cpp b/STL_Extension/test/STL_Extension/test_Compact_container_is_used.cpp
index aac89dc61d5..2d810602cde 100644
--- a/STL_Extension/test/STL_Extension/test_Compact_container_is_used.cpp
+++ b/STL_Extension/test/STL_Extension/test_Compact_container_is_used.cpp
@@ -15,7 +15,7 @@ public:
   {}
 
   void *   for_compact_container() const { return p_cc; }
-  void * & for_compact_container()       { return p_cc; }
+  void for_compact_container(void *p) { p_cc = p; }
 };
 
 int main()
diff --git a/STL_Extension/test/STL_Extension/test_Concurrent_compact_container.cpp b/STL_Extension/test/STL_Extension/test_Concurrent_compact_container.cpp
index 84a65304eb1..95f92dba74c 100644
--- a/STL_Extension/test/STL_Extension/test_Concurrent_compact_container.cpp
+++ b/STL_Extension/test/STL_Extension/test_Concurrent_compact_container.cpp
@@ -67,7 +67,7 @@ public:
   bool operator< (const Node_2 &n) const { return rnd <  n.rnd; }
 
   void *   for_compact_container() const { return p_cc; }
-  void * & for_compact_container()       { return p_cc; }
+  void for_compact_container(void *p) { p_cc = p; }
 };
 
 template < class Cont >
diff --git a/TDS_2/doc/TDS_2/Concepts/TriangulationDSFaceBase_2.h b/TDS_2/doc/TDS_2/Concepts/TriangulationDSFaceBase_2.h
index 8ef6ea99deb..71ae4e585af 100644
--- a/TDS_2/doc/TDS_2/Concepts/TriangulationDSFaceBase_2.h
+++ b/TDS_2/doc/TDS_2/Concepts/TriangulationDSFaceBase_2.h
@@ -183,7 +183,7 @@ void * for_compact_container() const;
 /*!
 
 */ 
-void * & for_compact_container(); 
+void for_compact_container(void *p);
 
 /// @}
 
diff --git a/TDS_2/doc/TDS_2/Concepts/TriangulationDSVertexBase_2.h b/TDS_2/doc/TDS_2/Concepts/TriangulationDSVertexBase_2.h
index e7915a48888..dcd30aa9f07 100644
--- a/TDS_2/doc/TDS_2/Concepts/TriangulationDSVertexBase_2.h
+++ b/TDS_2/doc/TDS_2/Concepts/TriangulationDSVertexBase_2.h
@@ -118,7 +118,7 @@ void * for_compact_container() const;
 /*!
 
 */ 
-void * & for_compact_container(); 
+void for_compact_container(void* p);
 
 /// @}
 
diff --git a/TDS_2/include/CGAL/Triangulation_ds_face_base_2.h b/TDS_2/include/CGAL/Triangulation_ds_face_base_2.h
index 8de378eec8f..8aeb12f876e 100644
--- a/TDS_2/include/CGAL/Triangulation_ds_face_base_2.h
+++ b/TDS_2/include/CGAL/Triangulation_ds_face_base_2.h
@@ -79,7 +79,7 @@ public:
   
    // For use by Compact_container.
   void * for_compact_container() const {return N[0].for_compact_container(); }
-  void * & for_compact_container()     { return N[0].for_compact_container();}
+  void for_compact_container(void* p) { N[0].for_compact_container(p);}
 
 
   static int ccw(int i) {return Triangulation_cw_ccw_2::ccw(i);}
diff --git a/TDS_2/include/CGAL/Triangulation_ds_vertex_base_2.h b/TDS_2/include/CGAL/Triangulation_ds_vertex_base_2.h
index 6b4906e6566..ceabf7c4294 100644
--- a/TDS_2/include/CGAL/Triangulation_ds_vertex_base_2.h
+++ b/TDS_2/include/CGAL/Triangulation_ds_vertex_base_2.h
@@ -49,7 +49,7 @@ public:
 
     // For use by the Compact_container.
   void *   for_compact_container() const { return _f.for_compact_container(); }
-  void * & for_compact_container()       { return _f.for_compact_container(); }
+  void for_compact_container(void* p) { _f.for_compact_container(p); }
 
 private:
   Face_handle _f;
diff --git a/TDS_3/doc/TDS_3/Concepts/TriangulationDSCellBase_3.h b/TDS_3/doc/TDS_3/Concepts/TriangulationDSCellBase_3.h
index 2856e1d70bd..9b9bffacd71 100644
--- a/TDS_3/doc/TDS_3/Concepts/TriangulationDSCellBase_3.h
+++ b/TDS_3/doc/TDS_3/Concepts/TriangulationDSCellBase_3.h
@@ -136,7 +136,7 @@ void * for_compact_container() const;
 /*!
 
 */ 
-void * & for_compact_container(); 
+void for_compact_container(void *p);
 
 /// @}
 
diff --git a/TDS_3/doc/TDS_3/Concepts/TriangulationDSVertexBase_3.h b/TDS_3/doc/TDS_3/Concepts/TriangulationDSVertexBase_3.h
index e1d35cb88fc..c7b68ec9175 100644
--- a/TDS_3/doc/TDS_3/Concepts/TriangulationDSVertexBase_3.h
+++ b/TDS_3/doc/TDS_3/Concepts/TriangulationDSVertexBase_3.h
@@ -116,7 +116,7 @@ void * for_compact_container() const;
 /*!
 
 */ 
-void * & for_compact_container(); 
+void for_compact_container(void *);
 
 /*!
 Inputs the non-combinatorial information given by the vertex. 
diff --git a/TDS_3/include/CGAL/Triangulation_ds_cell_base_3.h b/TDS_3/include/CGAL/Triangulation_ds_cell_base_3.h
index e6ad17ca862..f8449c7eb8c 100644
--- a/TDS_3/include/CGAL/Triangulation_ds_cell_base_3.h
+++ b/TDS_3/include/CGAL/Triangulation_ds_cell_base_3.h
@@ -180,7 +180,7 @@ public:
 
   // For use by Compact_container.
   void * for_compact_container() const { return N[0].for_compact_container(); }
-  void * & for_compact_container()     { return N[0].for_compact_container(); }
+  void for_compact_container(void* p) { N[0].for_compact_container(p); }
 
   // TDS internal data access functions.
         TDS_data& tds_data()       { return _tds_data; }
diff --git a/TDS_3/include/CGAL/Triangulation_ds_vertex_base_3.h b/TDS_3/include/CGAL/Triangulation_ds_vertex_base_3.h
index d6c5d38a057..f338340b50a 100644
--- a/TDS_3/include/CGAL/Triangulation_ds_vertex_base_3.h
+++ b/TDS_3/include/CGAL/Triangulation_ds_vertex_base_3.h
@@ -59,8 +59,8 @@ public:
   // For use by the Compact_container.
   void *   for_compact_container() const
   { return _c.for_compact_container(); }
-  void * & for_compact_container()
-  { return _c.for_compact_container(); }
+  void for_compact_container(void* p)
+  { _c.for_compact_container(p); }
 
 private:
   Cell_handle _c;
diff --git a/Triangulation/doc/Triangulation/Concepts/TriangulationDSFullCell.h b/Triangulation/doc/Triangulation/Concepts/TriangulationDSFullCell.h
index df05688010a..b25a2a7a81c 100644
--- a/Triangulation/doc/Triangulation/Concepts/TriangulationDSFullCell.h
+++ b/Triangulation/doc/Triangulation/Concepts/TriangulationDSFullCell.h
@@ -107,7 +107,7 @@ void * for_compact_container() const;
 /*!
 
 */
-void * & for_compact_container();
+void for_compact_container(void *p);
 
 /// @}
 
diff --git a/Triangulation/doc/Triangulation/Concepts/TriangulationDSVertex.h b/Triangulation/doc/Triangulation/Concepts/TriangulationDSVertex.h
index 0366254ca89..903da560d1c 100644
--- a/Triangulation/doc/Triangulation/Concepts/TriangulationDSVertex.h
+++ b/Triangulation/doc/Triangulation/Concepts/TriangulationDSVertex.h
@@ -106,7 +106,7 @@ void * for_compact_container() const;
 /*!
 
 */
-void * & for_compact_container();
+void for_compact_container(void *p);
 
 /// @}
 
diff --git a/Triangulation/include/CGAL/TDS_full_cell_default_storage_policy.h b/Triangulation/include/CGAL/TDS_full_cell_default_storage_policy.h
index d5f0735c8e8..3b6508f6017 100644
--- a/Triangulation/include/CGAL/TDS_full_cell_default_storage_policy.h
+++ b/Triangulation/include/CGAL/TDS_full_cell_default_storage_policy.h
@@ -44,7 +44,7 @@ struct TFC_data< Vertex_handle, Full_cell_handle, Dimen, TDS_full_cell_default_s
     : vertices_(dmax+1), neighbors_(dmax+1)
     {}
     void*   for_compact_container() const { return vertices_.for_compact_container(); }
-    void* & for_compact_container()       { return vertices_.for_compact_container(); }
+    void    for_compact_container(void *p){ vertices_.for_compact_container(p); }
     int dimension() const { return ( vertices_.size() - 1 ); }
     void set_mirror_index(const int, const int) {}
 #ifdef BOOST_NO_INT64_T
diff --git a/Triangulation/include/CGAL/Triangulation_ds_full_cell.h b/Triangulation/include/CGAL/Triangulation_ds_full_cell.h
index 125cc2e443f..83b48a441d5 100644
--- a/Triangulation/include/CGAL/Triangulation_ds_full_cell.h
+++ b/Triangulation/include/CGAL/Triangulation_ds_full_cell.h
@@ -204,7 +204,7 @@ public:
     TDS_data & tds_data() { return tds_data_; } /* Concept */
 
     void*   for_compact_container() const { return combinatorics_.for_compact_container(); }
-    void* & for_compact_container() { return combinatorics_.for_compact_container(); }
+    void    for_compact_container(void* p){ combinatorics_.for_compact_container(p); }
 
     bool is_valid(bool verbose = false, int = 0) const /* Concept */
     {
diff --git a/Triangulation/include/CGAL/Triangulation_ds_vertex.h b/Triangulation/include/CGAL/Triangulation_ds_vertex.h
index a4f47d05647..c57bfbed51a 100644
--- a/Triangulation/include/CGAL/Triangulation_ds_vertex.h
+++ b/Triangulation/include/CGAL/Triangulation_ds_vertex.h
@@ -102,7 +102,7 @@ public:
 public: // FOR MEMORY MANAGEMENT
 
     void*   for_compact_container() const { return full_cell_.for_compact_container(); }
-    void* & for_compact_container()       { return full_cell_.for_compact_container(); }
+    void    for_compact_container(void *p){ full_cell_.for_compact_container(p); }
 
 };  // end of Triangulation_ds_vertex
 
diff --git a/Triangulation/include/CGAL/internal/Static_or_dynamic_array.h b/Triangulation/include/CGAL/internal/Static_or_dynamic_array.h
index f198464e874..54fca5abaea 100644
--- a/Triangulation/include/CGAL/internal/Static_or_dynamic_array.h
+++ b/Triangulation/include/CGAL/internal/Static_or_dynamic_array.h
@@ -66,9 +66,9 @@ struct S_or_D_array< Containee, Dimension_tag< D >, WithCompactContainerHelper >
     {
         return (*this)[0].for_compact_container();
     }
-    void* & for_compact_container()
+    void    for_compact_container(void *p)
     {
-        return (*this)[0].for_compact_container();
+        (*this)[0].for_compact_container(p);
     }
 };
 
@@ -101,7 +101,7 @@ struct S_or_D_array< Containee, Dynamic_dimension_tag, true >
     {}
     void* fcc_;
     void*   for_compact_container() const { return fcc_; }
-    void* & for_compact_container()       { return fcc_; }
+    void    for_compact_container(void* p)       { fcc_ = p; }
 };
 
 } // end of namespace internal