diff --git a/Scale_space_reconstruction_3/include/CGAL/Scale_space_reconstruction_3/Scale_space_surface_reconstruction_3_impl.h b/Scale_space_reconstruction_3/include/CGAL/Scale_space_reconstruction_3/Scale_space_surface_reconstruction_3_impl.h
index db26ec4458a..8da661da552 100644
--- a/Scale_space_reconstruction_3/include/CGAL/Scale_space_reconstruction_3/Scale_space_surface_reconstruction_3_impl.h
+++ b/Scale_space_reconstruction_3/include/CGAL/Scale_space_reconstruction_3/Scale_space_surface_reconstruction_3_impl.h
@@ -393,7 +393,6 @@ Scale_space_surface_reconstruction_3<Gt,FS,Sh,wA,Ct>::
 increase_scale( unsigned int iterations ) {
     typedef std::vector< unsigned int >		CountVec;
     typedef std::map<Point, std::size_t>			PIMap;
-    typedef std::vector<Point>              Pointset;
 
     // This method must be called after filling the point collection.
     if( iterations == 0 || _tree.empty() ) return;
@@ -401,10 +400,6 @@ increase_scale( unsigned int iterations ) {
     if( !has_neighborhood_squared_radius() )
         estimate_neighborhood_squared_radius();
 
-    // To enable concurrent processing, we maintain two data structures:
-    // a search tree and a vector for the points after smoothing.
-    Pointset points;
-    points.assign( _tree.begin(), _tree.end() );
 
     for( unsigned int iter = 0; iter < iterations; ++iter ) {
         if( !_tree.is_built() )
@@ -413,21 +408,21 @@ increase_scale( unsigned int iterations ) {
         // Collect the number of neighbors of each point.
         // This can be done concurrently.
         CountVec neighbors( _tree.size(), 0 );
-        try_parallel( ComputeNN( points, _tree, _squared_radius, neighbors ), 0, _tree.size() );
+        try_parallel( ComputeNN( _points, _tree, _squared_radius, neighbors ), 0, _tree.size() );
 
         // Construct a mapping from each point to its index.
         PIMap indices;
         std::size_t index = 0;
-        for( typename Pointset::const_iterator pit = points.begin(); pit != points.end(); ++pit, ++index)
+        for( typename Pointset::const_iterator pit = _points.begin(); pit != _points.end(); ++pit, ++index)
             indices[ *pit ] = index;
 
         // Compute the tranformed point locations.
         // This can be done concurrently.
-        try_parallel( AdvanceSS( _tree, neighbors, indices, points ), 0, _tree.size() );
+        try_parallel( AdvanceSS( _tree, neighbors, indices, _points ), 0, _tree.size() );
 
         // Put the new points back in the tree.
         _tree.clear();
-        _tree.insert( points.begin(), points.end() );
+        _tree.insert( _points.begin(), _points.end() );
     }
 }
 
diff --git a/Scale_space_reconstruction_3/include/CGAL/Scale_space_surface_reconstruction_3.h b/Scale_space_reconstruction_3/include/CGAL/Scale_space_surface_reconstruction_3.h
index 2df12f24502..f0e01b8a081 100644
--- a/Scale_space_reconstruction_3/include/CGAL/Scale_space_surface_reconstruction_3.h
+++ b/Scale_space_reconstruction_3/include/CGAL/Scale_space_surface_reconstruction_3.h
@@ -201,6 +201,9 @@ private:
     // The shells can be accessed through iterators to the surface.
     TripleIterSet   _shells;
 
+    typedef std::vector<Point> Pointset;
+    Pointset _points;
+
 public:
 /// \name Constructors
 /// \{
@@ -292,6 +295,7 @@ public:
                      typename boost::enable_if< CGAL::is_iterator<InputIterator> >::type* = NULL ) {
 #endif // DOXYGEN_RUNNING
 		_tree.insert( begin, end );
+                _points.insert(_points.end(), begin, end);
 	}
     
     /// inserts a point into the scale-space at the current scale.
@@ -310,6 +314,7 @@ public:
      */
 	void insert( const Point& p ) {
 		_tree.insert( p );
+                _points.push_back(p);
 	}
     
     /// clears the stored scale-space surface reconstruction data.
@@ -803,20 +808,20 @@ public:
 /// \name Iterators
 /// \{
     /// gives an iterator to the first point at the current scale.
-    Point_const_iterator points_begin() const { return _tree.begin(); }
+    Point_const_iterator points_begin() const { return _points.begin(); }
     /// gives an iterator to the first point at the current scale.
     /** \warning Changes to the scale-space do not cause an automatic update to
      *  the surface.
      */
-    Point_iterator points_begin() { return _tree.begin(); }
+    Point_iterator points_begin() { return _points.begin(); }
 
     /// gives a past-the-end iterator of the points at the current scale.
-    Point_const_iterator points_end() const { return _tree.end(); }
+    Point_const_iterator points_end() const { return _points.end(); }
     /// gives a past-the-end iterator of the points at the current scale.
     /** \warning Changes to the scale-space do not cause an automatic update to
      *  the surface.
      */
-    Point_iterator points_end() { return _tree.end(); }
+    Point_iterator points_end() { return _points.end(); }
 
     /// gives an iterator to the first triple in the surface.
     Triple_const_iterator surface_begin() const { return _surface.begin(); }