diff --git a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_cleaning_plugin.cpp b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_cleaning_plugin.cpp
index 9d49bc8f116..eaf567abc91 100644
--- a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_cleaning_plugin.cpp
+++ b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_cleaning_plugin.cpp
@@ -80,6 +80,9 @@ void Point_set_demo_cleaning_plugin::on_actionOutlierRemoval_triggered()
                                         removed_percentage),
                   points->end());
 
+    // Scott Meyer's "swap trick" to trim excess capacity
+    Point_set(points).swap(points);
+
     points->invalidate_bounds();
     if (areOriented)
       points->unoriented_points_begin() = points->end();
diff --git a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_normal_estimation_plugin.cpp b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_normal_estimation_plugin.cpp
index f7821c71e37..53bf4b5d832 100644
--- a/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_normal_estimation_plugin.cpp
+++ b/Surface_reconstruction_points_3/demo/Surface_reconstruction_points_3/Point_set_demo/Point_set_demo_normal_estimation_plugin.cpp
@@ -122,11 +122,18 @@ void Point_set_demo_normal_estimation_plugin::on_actionNormalEstimation_triggere
 
       // mst_orient_normals() requires an iterator over points
       // + property maps to access each point's index, position and normal.
-      CGAL::mst_orient_normals(points->begin(), points->end(),
-                              CGAL::make_dereference_property_map(points->begin()),
-                              CGAL::make_normal_vector_property_map(points->begin()),
-                              CGAL::make_index_property_map(*points),
-                              dialog.orientationNbNeighbors());
+      Point_set::iterator unoriented_points_begin = 
+        CGAL::mst_orient_normals(points->begin(), points->end(),
+                                CGAL::make_dereference_property_map(points->begin()),
+                                CGAL::make_normal_vector_property_map(points->begin()),
+                                CGAL::make_index_property_map(*points),
+                                dialog.orientationNbNeighbors());
+
+      // Delete points with unoriented normals
+      points.erase(unoriented_points_begin, points.end());
+              
+      // Optional: Scott Meyer's "swap trick" to trim excess capacity
+      Point_set(points).swap(points);
 
       long memory = CGAL::Memory_sizer().virtual_size();
       std::cerr << "done: " << task_timer.time() << " seconds, "