diff --git a/NewKernel_d/include/CGAL/Kernel_d/Cartesian_LA_base.h b/NewKernel_d/include/CGAL/Kernel_d/Cartesian_LA_base.h
index 192a3024b5b..482a8912b07 100644
--- a/NewKernel_d/include/CGAL/Kernel_d/Cartesian_LA_base.h
+++ b/NewKernel_d/include/CGAL/Kernel_d/Cartesian_LA_base.h
@@ -64,6 +64,8 @@ struct Cartesian_LA_base_d : public Dimension_base<Dim_>
     template<class, class=void> struct Type {};
     template<class D> struct Type< Point_tag, D> { typedef Vector_ type; };
     template<class D> struct Type<Vector_tag, D> { typedef Vector_ type; };
+    template<class D> struct Type<    RT_tag, D> { typedef      RT type; };
+    template<class D> struct Type<    FT_tag, D> { typedef      FT type; };
 
     typedef typeset<Point_tag>
       ::add<Vector_tag>::type
diff --git a/NewKernel_d/include/CGAL/Kernel_d/Cartesian_change_FT.h b/NewKernel_d/include/CGAL/Kernel_d/Cartesian_change_FT.h
index f906581e2eb..d9a05bb0dad 100644
--- a/NewKernel_d/include/CGAL/Kernel_d/Cartesian_change_FT.h
+++ b/NewKernel_d/include/CGAL/Kernel_d/Cartesian_change_FT.h
@@ -48,9 +48,9 @@ struct Cartesian_change_FT_base : public
     };
     */
 
-    template<class Tag,class Type_>
+    template<class Tag_,class Type_>
     struct Construct_cartesian_const_iterator_ {
-	    typedef typename Get_functor<Kernel_base, Tag>::type Functor_base;
+	    typedef typename Get_functor<Kernel_base, Tag_>::type Functor_base;
 	    Construct_cartesian_const_iterator_(){}
 	    Construct_cartesian_const_iterator_(Self const&r):f(r){}
 	    Functor_base f;
@@ -67,9 +67,9 @@ struct Cartesian_change_FT_base : public
     typedef Construct_cartesian_const_iterator_<Construct_ttag<Point_cartesian_const_iterator_tag>,Point_cartesian_const_iterator> Construct_point_cartesian_const_iterator;
     typedef Construct_cartesian_const_iterator_<Construct_ttag<Vector_cartesian_const_iterator_tag>,Vector_cartesian_const_iterator> Construct_vector_cartesian_const_iterator;
 
-    template<class Tag>
+    template<class Tag_>
     struct Compute_cartesian_coordinate {
-	    typedef typename Get_functor<Kernel_base, Tag>::type Functor_base;
+	    typedef typename Get_functor<Kernel_base, Tag_>::type Functor_base;
 	    Compute_cartesian_coordinate(){}
 	    Compute_cartesian_coordinate(Self const&r):f(r){}
 	    Functor_base f;
diff --git a/NewKernel_d/include/CGAL/Kernel_d/Define_kernel_types.h b/NewKernel_d/include/CGAL/Kernel_d/Define_kernel_types.h
index 42e9e84b1c4..bbf981b8848 100644
--- a/NewKernel_d/include/CGAL/Kernel_d/Define_kernel_types.h
+++ b/NewKernel_d/include/CGAL/Kernel_d/Define_kernel_types.h
@@ -10,10 +10,10 @@
 
 namespace CGAL {
   namespace internal {
-    template<class K,class Tag,bool=iterator_tag_traits<Tag>::is_iterator>
-      struct Type_or_iter : K::template Type<Tag> {};
-    template<class K,class Tag>
-      struct Type_or_iter<K, Tag, true> : K::template Iterator<Tag> {};
+    template<class K,class Tag_,bool=iterator_tag_traits<Tag_>::is_iterator>
+      struct Type_or_iter : K::template Type<Tag_> {};
+    template<class K,class Tag_>
+      struct Type_or_iter<K, Tag_, true> : K::template Iterator<Tag_> {};
   }
   template<class K, class Base=K, class List=typename typeset_union<typename K::Object_list,typename K::Iterator_list>::type> struct Define_kernel_types;
   template<class K, class Base>
diff --git a/NewKernel_d/include/CGAL/Kernel_d/KernelD_converter.h b/NewKernel_d/include/CGAL/Kernel_d/KernelD_converter.h
index f53eaed3998..5a4b45bbf4c 100644
--- a/NewKernel_d/include/CGAL/Kernel_d/KernelD_converter.h
+++ b/NewKernel_d/include/CGAL/Kernel_d/KernelD_converter.h
@@ -52,13 +52,13 @@ template<class Final_, class K1, class K2, class List>
 class KernelD_converter_
 : public KernelD_converter_<Final_,K1,K2,typename List::tail>
 {
-	typedef typename List::head Tag;
+	typedef typename List::head Tag_;
 	typedef typename List::tail Rest;
 	typedef KernelD_converter_<Final_,K1,K2,Rest> Base;
-	typedef typename Get_type<K1,Tag>::type K1_Obj;
-	typedef typename Get_type<K2,Tag>::type K2_Obj;
-	typedef typename Get_functor<K1, Convert_ttag<Tag> >::type K1_Conv;
-	typedef KO_converter<Tag,K1,K2> KOC;
+	typedef typename Get_type<K1,Tag_>::type K1_Obj;
+	typedef typename Get_type<K2,Tag_>::type K2_Obj;
+	typedef typename Get_functor<K1, Convert_ttag<Tag_> >::type K1_Conv;
+	typedef KO_converter<Tag_,K1,K2> KOC;
 	typedef BOOSTD is_same<K1_Conv, Null_functor> no_converter;
 	typedef typename internal::Map_taglist_to_typelist<K1,Rest>::type::template contains<K1_Obj> duplicate;
 
@@ -68,7 +68,7 @@ class KernelD_converter_
 	  // If Point==Vector, keep only one conversion
 	  duplicate::value ||
 	  // For iterator objects, the default is make_transforming_iterator
-	  (iterator_tag_traits<Tag>::is_iterator && no_converter::value),
+	  (iterator_tag_traits<Tag_>::is_iterator && no_converter::value),
 	  Do_not_use,K1_Obj>::type argument_type;
 	//typedef typename KOC::argument_type K1_Obj;
 	//typedef typename KOC::result_type K2_Obj;
diff --git a/NewKernel_d/include/CGAL/Kernel_d/Kernel_d_interface.h b/NewKernel_d/include/CGAL/Kernel_d/Kernel_d_interface.h
index ddad6f1cfe1..799708205b6 100644
--- a/NewKernel_d/include/CGAL/Kernel_d/Kernel_d_interface.h
+++ b/NewKernel_d/include/CGAL/Kernel_d/Kernel_d_interface.h
@@ -79,12 +79,12 @@ template <class Base_> struct Kernel_d_interface : public Base_ {
 	  // Kernel_d requires a common iterator type for points and vectors
 	  // TODO: provide this mixed functor in preKernel?
 	  CGAL_static_assertion((boost::is_same<typename CGAL::decay<typename boost::result_of<CVI(Vector_d,CGAL::Begin_tag)>::type>::type, result_type>::value));
-	  template <class Tag>
-	  result_type operator()(Point_d const&p, Tag t)const{
+	  template <class Tag_>
+	  result_type operator()(Point_d const&p, Tag_ t)const{
 	    return CPI(this->kernel())(p,t);
 	  }
-	  template <class Tag>
-	  result_type operator()(Vector_d const&v, Tag t)const{
+	  template <class Tag_>
+	  result_type operator()(Vector_d const&v, Tag_ t)const{
 	    return CVI(this->kernel())(v,t);
 	  }
 
diff --git a/NewKernel_d/include/CGAL/functor_tags.h b/NewKernel_d/include/CGAL/functor_tags.h
index 94e99dda802..5c7370ee97e 100644
--- a/NewKernel_d/include/CGAL/functor_tags.h
+++ b/NewKernel_d/include/CGAL/functor_tags.h
@@ -41,16 +41,16 @@ namespace CGAL {
 	template<class>struct Convert_ttag {};
 
 	template<class> struct map_functor_type { typedef Misc_tag type; };
-	template<class Tag, class Obj, class Base> struct Typedef_tag_type;
-	//template<class Kernel, class Tag> struct Read_tag_type {};
+	template<class Tg, class Obj, class Base> struct Typedef_tag_type;
+	//template<class Kernel, class Tg> struct Read_tag_type {};
 
-	template<class Kernel, class Tag>
+	template<class Kernel, class Tg>
 	struct Provides_type
-	  : Has_type_different_from<Get_type<Kernel, Tag>, Null_type> {};
+	  : Has_type_different_from<Get_type<Kernel, Tg>, Null_type> {};
 
-	template<class Kernel, class Tag, class O=void>
+	template<class Kernel, class Tg, class O=void>
 	struct Provides_functor
-	  : Has_type_different_from<Get_functor<Kernel, Tag, O>, Null_functor> {};
+	  : Has_type_different_from<Get_functor<Kernel, Tg, O>, Null_functor> {};
 
 	template<class K, class List, bool=boost::mpl::empty<List>::type::value>
 	struct Provides_functors : boost::mpl::and_ <
@@ -67,25 +67,27 @@ namespace CGAL {
 	struct Provides_types<K, List, true> : boost::true_type {};
 
 	namespace internal { BOOST_MPL_HAS_XXX_TEMPLATE_DEF(Type) }
-	template<class Kernel, class Tag,
+	template<class Kernel, class Tg,
 	  bool = internal::has_Type<Kernel>::value /* false */>
 	struct Provides_type_i : boost::false_type {};
-	template<class Kernel, class Tag>
-	struct Provides_type_i <Kernel, Tag, true>
-	  : Has_type_different_from<typename Kernel::template Type<Tag>, Null_type> {};
+	template<class Kernel, class Tg>
+	struct Provides_type_i <Kernel, Tg, true>
+	  : Has_type_different_from<typename Kernel::template Type<Tg>, Null_type> {};
 
 	namespace internal { BOOST_MPL_HAS_XXX_TEMPLATE_DEF(Functor) }
-	template<class Kernel, class Tag, class O=void,
+	template<class Kernel, class Tg, class O=void,
 	  bool = internal::has_Functor<Kernel>::value /* false */>
 	struct Provides_functor_i : boost::false_type {};
-	template<class Kernel, class Tag, class O>
-	struct Provides_functor_i <Kernel, Tag, O, true>
-	  : Has_type_different_from<typename Kernel::template Functor<Tag, O>, Null_type> {};
+	template<class Kernel, class Tg, class O>
+	struct Provides_functor_i <Kernel, Tg, O, true>
+	  : Has_type_different_from<typename Kernel::template Functor<Tg, O>, Null_type> {};
 
 
-#define DECL_OBJ(X) struct X##_tag {}; \
+#define DECL_OBJ_(X) \
   template<class Obj,class Base> \
-  struct Typedef_tag_type<X##_tag, Obj, Base> : Base { typedef Obj X; };
+  struct Typedef_tag_type<X##_tag, Obj, Base> : Base { typedef Obj X; }
+#define DECL_OBJ(X) struct X##_tag {}; \
+  DECL_OBJ_(X)
 
   //namespace has_object { BOOST_MPL_HAS_XXX_TRAIT_DEF(X) }
   //template<class Kernel>
@@ -97,6 +99,14 @@ namespace CGAL {
 	DECL_OBJ(FT);
 	DECL_OBJ(RT);
 
+	//DECL_OBJ(Boolean); // FIXME: Boolean_tag is already taken, and is a template :-(
+	DECL_OBJ(Comparison_result);
+	DECL_OBJ(Sign);
+	DECL_OBJ(Orientation); // Note: duplicate with the functor tag!
+	DECL_OBJ(Oriented_side);
+	DECL_OBJ(Bounded_side);
+	DECL_OBJ(Angle);
+
 	DECL_OBJ(Vector);
 	DECL_OBJ(Point);
 	DECL_OBJ(Segment);
@@ -108,6 +118,7 @@ namespace CGAL {
 	DECL_OBJ(Iso_box);
 	DECL_OBJ(Bbox);
 	DECL_OBJ(Aff_transformation);
+#undef DECL_OBJ_
 #undef DECL_OBJ
 
 	template<class> struct is_NT_tag { enum { value = false }; };
@@ -140,7 +151,7 @@ namespace CGAL {
     typedef C##_tag container; \
   }; \
   template<class Obj,class Base> \
-  struct Typedef_tag_type<X##_tag, Obj, Base> : Base { typedef Obj X; };
+  struct Typedef_tag_type<X##_tag, Obj, Base> : Base { typedef Obj X; }
 
   //namespace has_object { BOOST_MPL_HAS_XXX_TRAIT_DEF(X) }
   //template<class Kernel>
@@ -187,8 +198,10 @@ namespace CGAL {
 #endif
 
 	//FIXME: choose a convention: prefix with Predicate_ ?
-#define DECL_PREDICATE(X) struct X##_tag {}; \
+#define DECL_PREDICATE_(X) \
 	template<>struct map_functor_type<X##_tag>{typedef Predicate_tag type;}
+#define DECL_PREDICATE(X) struct X##_tag {}; \
+	DECL_PREDICATE_(X)
 	DECL_PREDICATE(Less_point_cartesian_coordinate);
 	DECL_PREDICATE(Compare_point_cartesian_coordinate);
 	DECL_PREDICATE(Compare_distance);
@@ -196,7 +209,7 @@ namespace CGAL {
 	DECL_PREDICATE(Less_lexicographically);
 	DECL_PREDICATE(Less_or_equal_lexicographically);
 	DECL_PREDICATE(Equal_points);
-	DECL_PREDICATE(Orientation);
+	DECL_PREDICATE_(Orientation); // duplicate with the type
 	DECL_PREDICATE(Orientation_of_points);
 	DECL_PREDICATE(Orientation_of_vectors);
 	DECL_PREDICATE(Side_of_oriented_sphere);
diff --git a/NewKernel_d/include/CGAL/is_iterator.h b/NewKernel_d/include/CGAL/is_iterator.h
index 02cf09b0d14..591a26d86d6 100644
--- a/NewKernel_d/include/CGAL/is_iterator.h
+++ b/NewKernel_d/include/CGAL/is_iterator.h
@@ -48,8 +48,8 @@ template <class T,class U> struct is_iterator_type_<T,U,true> :
 template <class T> struct is_iterator :
 	internal::is_iterator_<typename boost::remove_cv<typename boost::remove_reference<T>::type>::type> {};
 
-template <class T,class Tag> struct is_iterator_type :
-	internal::is_iterator_type_<typename boost::remove_cv<typename boost::remove_reference<T>::type>::type,Tag> {};
+template <class T,class Tg> struct is_iterator_type :
+	internal::is_iterator_type_<typename boost::remove_cv<typename boost::remove_reference<T>::type>::type,Tg> {};
 
 template <class T,class U,bool=is_iterator<T>::value> struct is_iterator_to {
 	enum { value=false };
diff --git a/NewKernel_d/include/CGAL/marcutils.h b/NewKernel_d/include/CGAL/marcutils.h
index 38256545e8e..c825634d97a 100644
--- a/NewKernel_d/include/CGAL/marcutils.h
+++ b/NewKernel_d/include/CGAL/marcutils.h
@@ -231,14 +231,15 @@ BOOST_PP_REPEAT_FROM_TO(1, 8, CODE, _ )
 	};
 }
 
+// TODO: make a Cartesian-only variant
 #define CGAL_STRIP_PAREN_(...) __VA_ARGS__
 #define CGAL_STRIP_PAREN(...) CGAL_STRIP_PAREN_ __VA_ARGS__
 // What to do with O? pass it down to other functors or drop it?
-#define CGAL_KD_DEFAULT_FUNCTOR(Tag,Name,ReqTyp,ReqFun) \
+#define CGAL_KD_DEFAULT_FUNCTOR(Tg,Name,ReqTyp,ReqFun) \
     template <class K, class O> \
-    struct Get_functor<K, Tag, O, \
+    struct Get_functor<K, Tg, O, \
       typename boost::mpl::if_c< \
-        Provides_functor_i<K, Tag, O>::value \
+        Provides_functor_i<K, Tg, O>::value \
         || !Provides_types<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqTyp> >::value \
         || !Provides_functors<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqFun> >::value \
       , int, void>::type> \
@@ -247,11 +248,11 @@ BOOST_PP_REPEAT_FROM_TO(1, 8, CODE, _ )
     }
 
 // Not used yet, may need some changes.
-#define CGAL_KD_DEFAULT_TYPE(Tag,Name,ReqTyp,ReqFun) \
+#define CGAL_KD_DEFAULT_TYPE(Tg,Name,ReqTyp,ReqFun) \
     template <class K> \
-    struct Get_type<K, Tag, \
+    struct Get_type<K, Tg, \
       typename boost::mpl::if_c< \
-        Provides_type_i<K, Tag>::value \
+        Provides_type_i<K, Tg>::value \
         || !Provides_types<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqTyp> >::value \
         || !Provides_functors<K, boost::mpl::vector<CGAL_STRIP_PAREN_ ReqFun> >::value \
       , int, void>::type> \