diff --git a/STL_Extension/include/CGAL/Concurrent_compact_container.h b/STL_Extension/include/CGAL/Concurrent_compact_container.h
index e0ad2fb5333..0cda1fded36 100644
--- a/STL_Extension/include/CGAL/Concurrent_compact_container.h
+++ b/STL_Extension/include/CGAL/Concurrent_compact_container.h
@@ -36,6 +36,7 @@
 #include <CGAL/memory.h>
 #include <CGAL/iterator.h>
 #include <CGAL/CC_safe_handle.h>
+#include <CGAL/atomic.h>
 
 #include <tbb/tbb.h>
 
@@ -255,6 +256,11 @@ public:
   {
     std::swap(m_alloc, c.m_alloc);
     std::swap(m_capacity, c.m_capacity);
+    { // non-atomic swap
+      size_type other_size = c.m_size;
+      c.m_size = size_type(m_size);
+      m_size = other_size;
+    }
     std::swap(m_block_size, c.m_block_size);
     std::swap(m_first_item, c.m_first_item);
     std::swap(m_last_item, c.m_last_item);
@@ -445,6 +451,7 @@ private:
 #ifndef CGAL_NO_ASSERTIONS
     std::memset(&*x, 0, sizeof(T));
 #endif*/
+    --m_size;
     put_on_free_list(&*x, fl);
   }
 public:
@@ -465,9 +472,11 @@ public:
   // The complexity is O(size(free list = capacity-size)).
   void merge(Self &d);
 
-  // Do not call this function while others are inserting/erasing elements
+  // If `CGAL_NO_ATOMIC` is defined, do not call this function while others
+  // are inserting/erasing elements
   size_type size() const
   {
+#ifdef CGAL_NO_ATOMIC
     size_type size = m_capacity;
     for( typename Free_lists::iterator it_free_list = m_free_lists.begin() ;
          it_free_list != m_free_lists.end() ;
@@ -476,6 +485,9 @@ public:
       size -= it_free_list->size();
     }
     return size;
+#else // atomic can be used
+    return m_size;
+#endif
   }
 
   size_type max_size() const
@@ -587,6 +599,7 @@ private:
   {
     CGAL_assertion(type(ret) == USED);
     fl->dec_size();
+    ++m_size;
     return iterator(ret, 0);
   }
 
@@ -674,6 +687,7 @@ private:
     m_first_item = NULL;
     m_last_item  = NULL;
     m_all_items  = All_items();
+    m_size = 0;
   }
 
   allocator_type    m_alloc;
@@ -684,6 +698,11 @@ private:
   pointer           m_last_item;
   All_items         m_all_items;
   mutable Mutex     m_mutex;
+#ifdef CGAL_NO_ATOMIC
+  size_type         m_size;
+#else
+  CGAL::cpp11::atomic<size_type> m_size;
+#endif
 };
 
 template < class T, class Allocator >