diff --git a/Spatial_sorting/doc_tex/Spatial_sorting_ref/Multiscale_sort.tex b/Spatial_sorting/doc_tex/Spatial_sorting_ref/Multiscale_sort.tex
index 511c1d877e0..668ef1dc59b 100644
--- a/Spatial_sorting/doc_tex/Spatial_sorting_ref/Multiscale_sort.tex
+++ b/Spatial_sorting/doc_tex/Spatial_sorting_ref/Multiscale_sort.tex
@@ -14,7 +14,7 @@ stopping when there are less than \ccc{threshold} points.
 \ccTagFullDeclarations
 \ccCreationVariable{o}
 \ccCreation
-\ccConstructor{Multiscale_sort (const Sort &sort = Sort(), int threshold = 1, double ratio = 0.5)}{constructs an instance with \ccc{traits} as traits class instance.}
+\ccConstructor{Multiscale_sort (const Sort &sort = Sort(), std::ptrdiff_t threshold = 1, double ratio = 0.5)}{constructs an instance with \ccc{traits} as traits class instance.}
 \ccOperations
 \ccThree{void;;}{A}{}
 
diff --git a/Spatial_sorting/include/CGAL/Hilbert_sort_2.h b/Spatial_sorting/include/CGAL/Hilbert_sort_2.h
index a3176c71012..da0617c6608 100644
--- a/Spatial_sorting/include/CGAL/Hilbert_sort_2.h
+++ b/Spatial_sorting/include/CGAL/Hilbert_sort_2.h
@@ -21,9 +21,8 @@
 #define CGAL_HILBERT_SORT_2_H
 
 #include <CGAL/basic.h>
-
 #include <functional>
-
+#include <cstddef>
 #include <CGAL/Hilbert_sort_base.h>
 
 CGAL_BEGIN_NAMESPACE
@@ -83,13 +82,13 @@ public:
     
 private:
     Kernel _k;
-    int _limit;
+    std::ptrdiff_t _limit;
 
     template <int x, bool up> struct Cmp : public CGALi::Hilbert_cmp_2<Kernel,x,up>
     { Cmp (const Kernel &k) : CGALi::Hilbert_cmp_2<Kernel,x,up> (k) {} };
 
 public:
-    Hilbert_sort_2 (const Kernel &k = Kernel(), int limit = 1)
+    Hilbert_sort_2 (const Kernel &k = Kernel(), std::ptrdiff_t limit = 1)
         : _k(k), _limit (limit)
     {}
 
diff --git a/Spatial_sorting/include/CGAL/Hilbert_sort_3.h b/Spatial_sorting/include/CGAL/Hilbert_sort_3.h
index 2095b8577cb..ef8d738e8c7 100644
--- a/Spatial_sorting/include/CGAL/Hilbert_sort_3.h
+++ b/Spatial_sorting/include/CGAL/Hilbert_sort_3.h
@@ -21,9 +21,8 @@
 #define CGAL_HILBERT_SORT_3_H
 
 #include <CGAL/basic.h>
-
 #include <functional>
-
+#include <cstddef>
 #include <CGAL/Hilbert_sort_base.h>
 
 CGAL_BEGIN_NAMESPACE
@@ -97,13 +96,13 @@ public:
 
 private:
     Kernel _k;
-    int _limit;
+    std::ptrdiff_t _limit;
 
     template <int x, bool up> struct Cmp : public CGALi::Hilbert_cmp_3<Kernel,x,up>
     { Cmp (const Kernel &k) : CGALi::Hilbert_cmp_3<Kernel,x,up> (k) {} };
 
 public:
-    Hilbert_sort_3 (const Kernel &k = Kernel(), int limit = 1)
+    Hilbert_sort_3 (const Kernel &k = Kernel(), std::ptrdiff_t limit = 1)
         : _k(k), _limit (limit)
     {}
 
diff --git a/Spatial_sorting/include/CGAL/Multiscale_sort.h b/Spatial_sorting/include/CGAL/Multiscale_sort.h
index 9716907b935..0a1fbb14bb9 100644
--- a/Spatial_sorting/include/CGAL/Multiscale_sort.h
+++ b/Spatial_sorting/include/CGAL/Multiscale_sort.h
@@ -21,6 +21,8 @@
 #define CGAL_MULTISCALE_SORT_H
 
 #include <CGAL/basic.h>
+#include <iterator>
+#include <cstddef>
 
 CGAL_BEGIN_NAMESPACE
 
@@ -28,11 +30,11 @@ template <class Sort>
 class Multiscale_sort
 {
     Sort _sort;
-    int _threshold;
+    std::ptrdiff_t _threshold;
     double _ratio;
 
 public:
-    Multiscale_sort (const Sort &sort = Sort(), int threshold = 1, double ratio = 0.5)
+    Multiscale_sort (const Sort &sort = Sort(), std::ptrdiff_t threshold = 1, double ratio = 0.5)
         : _sort (sort), _threshold (threshold), _ratio (ratio)
     {
         CGAL_precondition (0. <= ratio && ratio <= 1.);
@@ -41,9 +43,10 @@ public:
     template <class RandomAccessIterator>
     void operator() (RandomAccessIterator begin, RandomAccessIterator end) const
     {
+	typedef typename std::iterator_traits<RandomAccessIterator>::difference_type difference_type;
         RandomAccessIterator middle = begin;
         if (end - begin >= _threshold) {
-            middle = begin + int ((end - begin) * _ratio);
+            middle = begin + difference_type ((end - begin) * _ratio);
             this->operator() (begin, middle);
         }
         _sort (middle, end);
@@ -52,4 +55,4 @@ public:
 
 CGAL_END_NAMESPACE
 
-#endif//CGAL_MULTISCALE_SORT_H
+#endif // CGAL_MULTISCALE_SORT_H