diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Arr_segment_data_traits_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Arr_segment_data_traits_2.h
index 46bcdf819db..41dea9ccf12 100644
--- a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Arr_segment_data_traits_2.h
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Arr_segment_data_traits_2.h
@@ -6,18 +6,18 @@ namespace CGAL {
 typedef std::pair<int, int> state;
 
 struct Segment_data_label {
-    Segment_data_label(state min_id, state max_id, CGAL::Comparison_result orientation, int origin):
+    Segment_data_label(state min_id, state max_id, Comparison_result orientation, int origin):
         _min_id(min_id), _max_id(max_id), _orientation(orientation), _origin(origin) {}
 
     Segment_data_label() {
         _min_id = state(-1, -1);
         _max_id = state(-1, -1);
-        _orientation = CGAL::SMALLER;
+        _orientation = SMALLER;
         _origin = -1;
     }
 
     int _origin;
-    CGAL::Comparison_result _orientation;
+    Comparison_result _orientation;
     state _min_id, _max_id;
 };
 
@@ -166,7 +166,7 @@ public:
             // Split the base curve into two.
             m_traits->split_2_object()(cv, p, c1, c2);
 
-            if (cv.data()._orientation == CGAL::SMALLER) {
+            if (cv.data()._orientation == SMALLER) {
                 c1.data()._min_id = cv.data()._min_id;
                 c2.data()._max_id = cv.data()._max_id;
             } else {
@@ -239,7 +239,7 @@ public:
 
             // code ONLY FOR SEGMENTS !!!!!!!!
 
-            std::list<CGAL::Object> base_objs;
+            std::list<Object> base_objs;
 
             m_traits->intersect_2_object()(xcv1, xcv2, std::back_inserter(base_objs));
 
@@ -248,7 +248,7 @@ public:
             }
 
             // Attach labels to the intersection objects.
-            std::list<CGAL::Object>::iterator obj_it;
+            std::list<Object>::iterator obj_it;
             const std::pair<Base_point_2, unsigned int> *base_pt;
             const Base_x_monotone_curve_2 *base_xcv;
 
@@ -258,7 +258,7 @@ public:
 
                 if (base_pt != NULL) {
                     // Attach an invalid label to an itersection point.
-                    *oi = CGAL::make_object
+                    *oi = make_object
                           (std::make_pair(Point_2(base_pt->first), base_pt->second));
                     ++oi;
                 } else {
@@ -266,7 +266,7 @@ public:
                     CGAL_assertion(base_xcv != NULL);
 
                     // Attach a merged label to the overlapping curve.
-                    *oi = CGAL::make_object(X_monotone_curve_2(*base_xcv, Segment_data_label(no_state, no_state, xcv1.data()._orientation, -1)));
+                    *oi = make_object(X_monotone_curve_2(*base_xcv, Segment_data_label(no_state, no_state, xcv1.data()._orientation, -1)));
                     ++oi;
                 }
             }
@@ -340,7 +340,7 @@ public:
         Point_2 operator()(const X_monotone_curve_2 &xcv) {
             Point_2 min_p = m_base_min_v(xcv);
 
-            if (xcv.label()._orientation == CGAL::SMALLER) {
+            if (xcv.label()._orientation == SMALLER) {
                 min_p.id = xcv.data()._min_id;
             } else {
                 min_p.id = xcv.data()._max_id;
@@ -382,7 +382,7 @@ public:
         Point_2 operator()(const X_monotone_curve_2 &xcv) const {
             Point_2 max_p = m_base_max_v(xcv);
 
-            if (xcv.label()._orientation == CGAL::SMALLER) {
+            if (xcv.label()._orientation == SMALLER) {
                 max_p.id = xcv.data()._max_id;
             } else {
                 max_p.id = xcv.data()._min_id;
diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Minkowski_sum_by_reduced_convolution_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Minkowski_sum_by_reduced_convolution_2.h
index a8903e2ffb4..ba21588be8a 100644
--- a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Minkowski_sum_by_reduced_convolution_2.h
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/Minkowski_sum_by_reduced_convolution_2.h
@@ -39,7 +39,7 @@ private:
 
     typedef Arr_default_dcel<Traits_2> Dcel;
 
-    typedef CGAL::Arrangement_with_history_2<Traits_2, Dcel> Arrangement_history_2;
+    typedef Arrangement_with_history_2<Traits_2, Dcel> Arrangement_history_2;
     typedef typename Arrangement_history_2::Halfedge Halfedge;
     typedef typename Arrangement_history_2::Vertex_iterator Vertex_iterator;
     typedef typename Arrangement_history_2::Edge_iterator Edge_iterator;
@@ -91,13 +91,13 @@ public:
     OutputIterator operator()(const Polygon_2 &pgn1, const Polygon_2 &pgn2,
                               Polygon_2 &sum_bound, OutputIterator sum_holes) {
 
-        CGAL::Timer timer;
+        Timer timer;
         timer.start();
 
         CGAL_precondition(pgn1.is_simple());
         CGAL_precondition(pgn2.is_simple());
-        CGAL_precondition(pgn1.orientation() == CGAL::COUNTERCLOCKWISE);
-        CGAL_precondition(pgn2.orientation() == CGAL::COUNTERCLOCKWISE);
+        CGAL_precondition(pgn1.orientation() == COUNTERCLOCKWISE);
+        CGAL_precondition(pgn2.orientation() == COUNTERCLOCKWISE);
 
         timer.stop();
         std::cout << timer.time() << " s: Preconditions" << std::endl;
@@ -123,7 +123,7 @@ public:
 
         // split the segments at their intersection points
         Arrangement_history_2 arr;
-        CGAL::insert(arr, reduced_conv.begin(), reduced_conv.end());
+        insert(arr, reduced_conv.begin(), reduced_conv.end());
 
         timer.stop();
         std::cout << timer.time() << " s: Arrangement" << std::endl;
@@ -208,7 +208,7 @@ private:
                     Point_2 start_point = get_point(i1, i2, points_map, pgn1, pgn2);
                     Point_2 end_point = get_point(i1, next_i2, points_map, pgn1, pgn2);
 
-                    CGAL::Comparison_result cres = f_compare_xy(start_point, end_point);
+                    Comparison_result cres = f_compare_xy(start_point, end_point);
                     Segment_2 conv_seg = Segment_2(typename Traits_2_A::Segment_2(start_point, end_point), Segment_data_label(state(i1, i2), state(i1, next_i2), cres, 1));
 
                     reduced_conv.push_back(conv_seg);
@@ -223,7 +223,7 @@ private:
                     Point_2 start_point = get_point(i1, i2, points_map, pgn1, pgn2);
                     Point_2 end_point = get_point(next_i1, i2, points_map, pgn1, pgn2);
 
-                    CGAL::Comparison_result cres = f_compare_xy(start_point, end_point);
+                    Comparison_result cres = f_compare_xy(start_point, end_point);
                     Segment_2 conv_seg = Segment_2(typename Traits_2_A::Segment_2(start_point, end_point), Segment_data_label(state(i1, i2), state(next_i1, i2), cres, 0));
                     reduced_conv.push_back(conv_seg);
                 }
@@ -313,7 +313,7 @@ private:
         Originating_curve_iterator segment_itr;
 
         for (segment_itr = arr.originating_curves_begin(he); segment_itr != arr.originating_curves_end(he); ++segment_itr) {
-            if (segment_itr->label()._orientation == (CGAL::Comparison_result)he->direction()) {
+            if (segment_itr->label()._orientation == (Comparison_result)he->direction()) {
                 return false;
             }
         }
@@ -341,7 +341,7 @@ private:
         while (++next_edge != current_edge) {
             Point_2 q = next_edge->target()->point();
             if (ear.has_on_bounded_side(q)) {
-                typename Kernel::FT distance = CGAL::squared_distance(q, v);
+                typename Kernel::FT distance = squared_distance(q, v);
                 if (min_distance == -1 || distance < min_distance) {
                     min_distance = distance;
                     min_q = q;
@@ -350,9 +350,9 @@ private:
         }
 
         if (min_distance != -1) {
-            return CGAL::midpoint(v, min_q);
+            return midpoint(v, min_q);
         } else {
-            return CGAL::centroid(ear);
+            return centroid(ear);
         }
     }
 };
diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_collision_detector_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_collision_detector_2.h
index 8c472c92807..ec5eb5da004 100644
--- a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_collision_detector_2.h
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_collision_detector_2.h
@@ -30,7 +30,7 @@ public:
             return true;
         }
 
-        Polygon_2 translated_p = transform(typename Kernel_::Aff_transformation_2(CGAL::Translation(), Vector_2(CGAL::ORIGIN, t)), m_p);
+        Polygon_2 translated_p = transform(typename Kernel_::Aff_transformation_2(Translation(), Vector_2(ORIGIN, t)), m_p);
         return (translated_p.has_on_bounded_side(*(m_q.vertices_begin())) || m_q.has_on_bounded_side(*(translated_p.vertices_begin())));
     }
 
diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_traits_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_traits_2.h
index 59a4980afbe..08494b78944 100644
--- a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_traits_2.h
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_traits_2.h
@@ -7,7 +7,7 @@ template <class R_> class Point_2;
 template <class R_> class Segment_2;
 
 double eps(double x) {
-    return CGAL::abs(CGAL::nextafter(x, DBL_MAX) - x);
+    return abs(nextafter(x, DBL_MAX) - x);
 }
 
 template<typename GeomTraits, typename AABB_primitive_>
@@ -15,7 +15,6 @@ class AABB_traits_2 {
 public:
     typedef AABB_traits_2<GeomTraits, AABB_primitive_> AT;
     typedef typename CGAL::Bbox_2 Bounding_box;
-    typedef typename CGAL::Object Object;
 
     typedef AABB_primitive_ Primitive;
     typedef typename Primitive::Id Id;
@@ -44,10 +43,10 @@ public:
     Construct_cartesian_const_iterator_3;
 
     AABB_traits_2(const Point &point, const Container &p, const Container &q): m_t_point(point), m_p(p), m_q(q) {
-        m_x_interval = Interval_nt<true>(CGAL::to_interval(point.x()));
-        m_y_interval = Interval_nt<true>(CGAL::to_interval(point.y()));
-        m_px = CGAL::to_double(point.x());
-        m_py = CGAL::to_double(point.y());
+        m_x_interval = Interval_nt<true>(to_interval(point.x()));
+        m_y_interval = Interval_nt<true>(to_interval(point.y()));
+        m_px = to_double(point.x());
+        m_py = to_double(point.y());
     };
 
     AABB_traits_2(): m_p(Container()), m_q(Container()) {
@@ -156,9 +155,9 @@ public:
 
             /* Code for faster bbox, needs to be tested
             // Get x max error.
-            double x_epsilon = CGAL::max(CGAL::max(eps(m_traits->m_px),eps(bbox.xmin())),eps(bbox.xmax()))*2;
+            double x_epsilon = max(max(eps(m_traits->m_px),eps(bbox.xmin())),eps(bbox.xmax()))*2;
             // Get y max error.
-            double y_epsilon = CGAL::max(CGAL::max(eps(m_traits->m_py),eps(bbox.ymin())),eps(bbox.ymax()))*2;
+            double y_epsilon = max(max(eps(m_traits->m_py),eps(bbox.ymin())),eps(bbox.ymax()))*2;
             double t_left = (m_traits->m_px + bbox.xmin())-x_epsilon;
             double t_right = (m_traits->m_px + bbox.xmax())+x_epsilon;
             double t_bottom = (m_traits->m_py + bbox.ymin())-y_epsilon;
@@ -172,15 +171,15 @@ public:
             double t_top = (m_traits->get_int_y() + bbox.ymax()).sup();
             Bounding_box t_box(t_left, t_bottom, t_right, t_top);
 
-            return CGAL::do_overlap(q, t_box);
+            return do_overlap(q, t_box);
         }
 
         bool operator()(const Primitive &q, const Bounding_box &bbox) const {
             /* Code for faster bbox, needs to be tested
             // Get x max error.
-            double x_epsilon = CGAL::max(CGAL::max(eps(m_traits->m_px),eps(bbox.xmin())),eps(bbox.xmax()))*2;
+            double x_epsilon = max(max(eps(m_traits->m_px),eps(bbox.xmin())),eps(bbox.xmax()))*2;
             // Get y max error.
-            double y_epsilon = CGAL::max(CGAL::max(eps(m_traits->m_py),eps(bbox.ymin())),eps(bbox.ymax()))*2;
+            double y_epsilon = max(max(eps(m_traits->m_py),eps(bbox.ymin())),eps(bbox.ymax()))*2;
             double t_left = (m_traits->m_px + bbox.xmin())-x_epsilon;
             double t_right = (m_traits->m_px + bbox.xmax())+x_epsilon;
             double t_bottom = (m_traits->m_py + bbox.ymin())-y_epsilon;
@@ -194,26 +193,26 @@ public:
             double t_top = (m_traits->get_int_y() + bbox.ymax()).sup();
             Bounding_box t_box(t_left, t_bottom, t_right, t_top);
 
-            return CGAL::do_overlap(q.datum().bbox(), t_box);
+            return do_overlap(q.datum().bbox(), t_box);
         }
 
         bool operator()(const Bounding_box &q, const Primitive &pr) const {
 
-            typename Primitive::Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(CGAL::Translation(), Vector_2(CGAL::ORIGIN, m_traits->get_translation_point())));
-            return CGAL::do_overlap(q, tr_pr.bbox());
+            typename Primitive::Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(Translation(), Vector_2(ORIGIN, m_traits->get_translation_point())));
+            return do_overlap(q, tr_pr.bbox());
         }
 
         bool operator()(const Primitive &q, const Primitive &pr) const {
 
-            typename Primitive::Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(CGAL::Translation(), Vector_2(CGAL::ORIGIN, m_traits->get_translation_point())));
+            typename Primitive::Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(Translation(), Vector_2(ORIGIN, m_traits->get_translation_point())));
 
-            if (!CGAL::do_overlap(q.datum().bbox(), tr_pr.bbox())) {
+            if (!do_overlap(q.datum().bbox(), tr_pr.bbox())) {
                 return false;
             }
 
-            CGAL::Object intersection_object = GeomTraits().intersect_2_object()(q.datum(), tr_pr);
+            Object intersection_object = GeomTraits().intersect_2_object()(q.datum(), tr_pr);
 
-            if (const CGAL::Point_2<GeomTraits> *ipoint = CGAL::object_cast<CGAL::Point_2<GeomTraits> >(&intersection_object)) {
+            if (const CGAL::Point_2<GeomTraits> *ipoint = object_cast<CGAL::Point_2<GeomTraits> >(&intersection_object)) {
                 // handle weak intersections
                 bool has_weak_intersection = false;
                 bool p_intersect = false;
@@ -259,9 +258,9 @@ public:
                 }
             }
 
-            if (const CGAL::Segment_2<GeomTraits> *iseg = CGAL::object_cast<CGAL::Segment_2<GeomTraits> >(&intersection_object)) { // we have overlapping segments
-                CGAL::Comparison_result c1 = CGAL::compare_xy(tr_pr.source(), tr_pr.target());
-                CGAL::Comparison_result c2 = CGAL::compare_xy(q.datum().source(), q.datum().target());
+            if (const CGAL::Segment_2<GeomTraits> *iseg = object_cast<CGAL::Segment_2<GeomTraits> >(&intersection_object)) { // we have overlapping segments
+                Comparison_result c1 = compare_xy(tr_pr.source(), tr_pr.target());
+                Comparison_result c2 = compare_xy(q.datum().source(), q.datum().target());
 
                 bool same_dir = (c1 == c2);
                 return same_dir;
@@ -277,7 +276,7 @@ public:
             Id itr_q = q.id();
             Id p_other = get_other_segment(p_intersect_start, itr_p, m_traits->get_p());
             Id q_other = get_other_segment(q_intersect_start, itr_q, m_traits->get_q());
-            Datum p_other_translated = (*p_other).transform(typename GeomTraits::Aff_transformation_2(CGAL::Translation(), Vector_2(CGAL::ORIGIN, m_traits->get_translation_point())));
+            Datum p_other_translated = (*p_other).transform(typename GeomTraits::Aff_transformation_2(Translation(), Vector_2(ORIGIN, m_traits->get_translation_point())));
 
             if (p_intersect && !q_intersect) {
                 if (p_intersect_start) {
@@ -378,7 +377,7 @@ public:
         operator()(const Query &query, const typename AT::Primitive &primitive) const {
             typedef boost::optional<Object_and_primitive_id> Intersection;
 
-            CGAL::Object object = GeomTraits().intersect_2_object()(primitive.datum(), query);
+            Object object = GeomTraits().intersect_2_object()(primitive.datum(), query);
 
             if (object.empty()) {
                 return Intersection();
@@ -402,7 +401,7 @@ public:
 
         Point operator()(const Point &p, const Primitive &pr, const Point &bound) const {
             // seems to be unused:
-            //return CGAL::nearest_point_2(p, pr.datum(), bound);
+            //return nearest_point_2(p, pr.datum(), bound);
             return p;
         }
     };
@@ -419,11 +418,11 @@ public:
     public:
 
         template <class Solid>
-        CGAL::Comparison_result operator()(const Point &p, const Solid &pr, const Point &bound) const {
+        Comparison_result operator()(const Point &p, const Solid &pr, const Point &bound) const {
             return GeomTraits().do_intersect_2_object()
                    (GeomTraits().construct_sphere_2_object()
                     (p, GeomTraits().compute_squared_distance_2_object()(p, bound)), pr) ?
-                   CGAL::SMALLER : CGAL::LARGER;
+                   SMALLER : LARGER;
         }
     };
 
diff --git a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_tree_2.h b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_tree_2.h
index 69095a5f27a..e2afb801925 100644
--- a/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_tree_2.h
+++ b/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/new/aabb/AABB_tree_2.h
@@ -468,7 +468,7 @@ private:
 
         bool do_intersect(const Point &query, const Node &node) const {
             return AABBTraits().compare_distance_object()
-                   (query, node.bbox(), m_closest_point) == CGAL::SMALLER;
+                   (query, node.bbox(), m_closest_point) == SMALLER;
         }
 
         Point closest_point() const {