diff --git a/STL_Extension/include/CGAL/Base_with_time_stamp.h b/STL_Extension/include/CGAL/Base_with_time_stamp.h
index 0ef77b262be..7dff85ab6d1 100644
--- a/STL_Extension/include/CGAL/Base_with_time_stamp.h
+++ b/STL_Extension/include/CGAL/Base_with_time_stamp.h
@@ -18,7 +18,7 @@ namespace CGAL {
 
 template <typename Base>
 class Base_with_time_stamp : public Base {
-  std::size_t time_stamp_ = -1;
+  std::size_t time_stamp_ = 0;
 public:
   using Base::Base;
 
diff --git a/STL_Extension/include/CGAL/Compact_container.h b/STL_Extension/include/CGAL/Compact_container.h
index e6e41515ff4..e82a33412d9 100644
--- a/STL_Extension/include/CGAL/Compact_container.h
+++ b/STL_Extension/include/CGAL/Compact_container.h
@@ -382,10 +382,17 @@ public:
 
     pointer ret = free_list;
     free_list = clean_pointee(ret);
+    std::size_t ts;
+    if constexpr (Time_stamper::has_timestamp) {
+      ts = ret->time_stamp();
+    }
     new (ret) value_type(args...);
+    if constexpr (Time_stamper::has_timestamp) {
+      ret->set_time_stamp(ts);
+    }
+    Time_stamper::set_time_stamp(ret, time_stamp);
     CGAL_assertion(type(ret) == USED);
     ++size_;
-    Time_stamper::set_time_stamp(ret, time_stamp);
     return iterator(ret, 0);
   }
 
@@ -424,7 +431,14 @@ public:
 
     CGAL_precondition(type(&*x) == USED);
     EraseCounterStrategy::increment_erase_counter(*x);
+    std::size_t ts;
+    if constexpr (Time_stamper::has_timestamp) {
+      ts = x->time_stamp();
+    }
     std::allocator_traits<allocator_type>::destroy(alloc, &*x);
+    if constexpr (Time_stamper::has_timestamp) {
+      x->set_time_stamp(ts);
+    }
 
     put_on_free_list(&*x);
     --size_;
@@ -638,6 +652,9 @@ private:
   // Get the type of the pointee.
   static Type type(const_pointer ptr)
   {
+    if constexpr (Time_stamper::has_timestamp) {
+      return (Type)(ptr->time_stamp() >> Time_stamper::time_stamp_shift);
+    }
     char * p = (char *) Traits::pointer(*ptr);
     return (Type) (reinterpret_cast<std::ptrdiff_t>(p) -
                    reinterpret_cast<std::ptrdiff_t>(clean_pointer(p)));
@@ -646,6 +663,10 @@ private:
   // Sets the pointer part and the type of the pointee.
   static void set_type(pointer ptr, void * p, Type t)
   {
+    if constexpr (Time_stamper::has_timestamp) {
+      const auto ts = ptr->time_stamp() & ~(Time_stamper::time_stamp_mask);
+      ptr->set_time_stamp(ts | (static_cast<std::size_t>(t) << Time_stamper::time_stamp_shift));
+    }
     // This out of range compare is always true and causes lots of
     // unnecessary warnings.
     // CGAL_precondition(0 <= t && t < 4);
diff --git a/STL_Extension/include/CGAL/Time_stamper.h b/STL_Extension/include/CGAL/Time_stamper.h
index a1f2d30eb36..7afe7160eee 100644
--- a/STL_Extension/include/CGAL/Time_stamper.h
+++ b/STL_Extension/include/CGAL/Time_stamper.h
@@ -28,17 +28,28 @@ constexpr size_t rounded_down_log2(size_t n)
 template <typename T>
 struct Time_stamper
 {
+  static constexpr bool has_timestamp = true;
+  static constexpr int time_stamp_shift = sizeof(std::size_t) * CHAR_BIT - 2;
+  static constexpr std::size_t time_stamp_mask = std::size_t(0b11) << time_stamp_shift;
+  static constexpr std::size_t time_stamp_is_free_mask = std::size_t(0b001) << (time_stamp_shift - 1);
+
   static void initialize_time_stamp(T* pt) {
     pt->set_time_stamp(std::size_t(-1));
   }
 
+  static bool is_free(const T* pt)
+  {
+    return ( pt->time_stamp() & time_stamp_is_free_mask )!= 0;
+  }
+
   template <typename time_stamp_t>
   static void set_time_stamp(T* pt, time_stamp_t& time_stamp_) {
-    if(pt->time_stamp() == std::size_t(-1)) {
+    if(is_free(pt)) {
       const std::size_t new_ts = time_stamp_++;
       pt->set_time_stamp(new_ts);
     }
     else {
+      pt->set_time_stamp(pt->time_stamp() & ~time_stamp_mask);
       // else: the time stamp is re-used
 
       // Enforces that the time stamp is greater than the current value.
@@ -95,6 +106,7 @@ struct Time_stamper
 template <typename T>
 struct No_time_stamp
 {
+  static constexpr bool has_timestamp = false;
 public:
   template <typename time_stamp_t>
   static void set_time_stamp(T*, time_stamp_t&)  {}