diff --git a/Circular_kernel_2/Benchmarks/DxfArrayBenchmarks/benchmark.h b/Circular_kernel_2/Benchmarks/DxfArrayBenchmarks/benchmark.h
index 994e40ddb53..9a144bd89c5 100644
--- a/Circular_kernel_2/Benchmarks/DxfArrayBenchmarks/benchmark.h
+++ b/Circular_kernel_2/Benchmarks/DxfArrayBenchmarks/benchmark.h
@@ -260,14 +260,14 @@ private:
   	typedef typename CGAL::Arr_naive_point_location<Pmwx>        Point_location;
   	
 	std::cout << "memory size before construction" << mem_sizer.virtual_size() << std::endl;
-  	std::cout << "memory resident size before insert_curves()" << mem_sizer.resident_size () << std::endl;
+  	std::cout << "memory resident size before insert()" << mem_sizer.resident_size () << std::endl;
   	MemBefore = mem_sizer.virtual_size ()/1000;
 	Pmwx _pm;
   	Point_location _pl(_pm);
   	
 	try{
     		this->start(); 
-      		insert_curves(_pm,ac.begin(),ac.end());
+      		insert(_pm,ac.begin(),ac.end(),boost::false_type());
     		this->stop();
   	}
   	catch (...) {
@@ -280,8 +280,8 @@ private:
    	if (!fail){this->summarize(_pm.number_of_vertices(),_pm.number_of_halfedges());}
    	
         MemAfter = mem_sizer.virtual_size ()/1000;
-	std::cout << "memory size after insert_curves()" << mem_sizer.virtual_size () << std::endl; 
-    	std::cout << "memory resident size after insert_curves()" << mem_sizer.resident_size () << std::endl;
+	std::cout << "memory size after insert()" << mem_sizer.virtual_size () << std::endl; 
+    	std::cout << "memory resident size after insert()" << mem_sizer.resident_size () << std::endl;
 	_pm.clear();
     	
  }
diff --git a/Circular_kernel_2/Benchmarks/Input_data.h b/Circular_kernel_2/Benchmarks/Input_data.h
index a0fa4516681..3c9f9d34b1b 100644
--- a/Circular_kernel_2/Benchmarks/Input_data.h
+++ b/Circular_kernel_2/Benchmarks/Input_data.h
@@ -25,7 +25,7 @@ void _bench_input_grid(ArcContainer& ac){
   	
 	for(int i = 0; i < 20; i++){
     		for(int j = 0; j <20; j++){
-      			ac.push_back( Circle_2( Point_2(x + j*r, y + i*r), r*r));
+      			ac.push_back(typename CK::Circular_arc_2 (  Circle_2( Point_2(x + j*r, y + i*r), r*r)));
     		}
   	}
 }
@@ -42,7 +42,7 @@ void _bench_input_grid2(ArcContainer& ac){
  
   	for(int i = 0; i < 20; i++){
     		for(int j = 0; j < 20; j++){
-     			ac.push_back(Circle_2( Point_2(x + j*r, y + i*r), r*r));
+     			ac.push_back(typename CK::Circular_arc_2 ( Circle_2( Point_2(x + j*r, y + i*r), r*r) ));
     		}
   	}
 
@@ -51,7 +51,7 @@ void _bench_input_grid2(ArcContainer& ac){
   	
 	for(int i = 0; i < 20; i++){
     		for(int j = 0; j < 20; j++){
-      			ac.push_back( Circle_2( Point_2(x + j*r, y + i*r), r*r));
+      			ac.push_back(typename CK::Circular_arc_2 (  Circle_2( Point_2(x + j*r, y + i*r), r*r)));
     		}
   	}
 
@@ -77,7 +77,7 @@ void _bench_input_random(ArcContainter& arcs)
      		double y = theRandom.get_double(random_min,random_max);
      		double r = theRandom.get_double(0.1,random_max);
      		fout << x << " " << y << " " << r << " " ;
-    		arcs.push_back( Circle_2( Point_2(x,y), r*r));
+    		arcs.push_back(typename CK::Circular_arc_2 (  Circle_2( Point_2(x,y), r*r) ));
     	}
 	
 	fout.close();
@@ -94,7 +94,7 @@ void _bench_input_file(ArcContainter& arcs){
       	std::ifstream fin("random.inp");
       	for(int i = 0; i < 100 ; i++){
 		fin >> x >> y >> r ;
-         	arcs.push_back( Circle_2( Point_2(x,y), r*r));
+         	arcs.push_back(typename CK::Circular_arc_2 (  Circle_2( Point_2(x,y), r*r)));
       	}
       	
 	fin.close();
@@ -115,7 +115,7 @@ void _bench_input_rotation(ArcContainter& ac){
  		for(int i = 0; i < 5; i++){
     			for(int j = 0; j < 5; j++){
 				R = (r+k)*(r+k);
-     				ac.push_back( Circle_2( Point_2(x + i*r, y + j*r),R));
+     				ac.push_back(typename CK::Circular_arc_2 (  Circle_2( Point_2(x + i*r, y + j*r),R) ));
      			}
  		}
 	}
diff --git a/Circular_kernel_2/Benchmarks/arrangement_traits/benchmark.h b/Circular_kernel_2/Benchmarks/arrangement_traits/benchmark.h
index ba495588330..9ba0d3c9522 100644
--- a/Circular_kernel_2/Benchmarks/arrangement_traits/benchmark.h
+++ b/Circular_kernel_2/Benchmarks/arrangement_traits/benchmark.h
@@ -206,7 +206,7 @@ class Bench
   typedef typename CGAL::Arrangement_2<Traits>                 Pmwx;
   typedef typename CGAL::Arr_naive_point_location<Pmwx>        Point_location;
   std::cout << "memory size before construction" << mem_sizer.virtual_size() << std::endl;
-  std::cout << "memory resident size before insert_curves()" << mem_sizer.resident_size () << std::endl;
+  std::cout << "memory resident size before insert()" << mem_sizer.resident_size () << std::endl;
   Pmwx _pm;
   Point_location _pl(_pm);
   
@@ -214,7 +214,7 @@ class Bench
   try{
     this->start();
     
-      insert_curves(_pm,ac.begin(),ac.end());
+      insert(_pm,ac.begin(),ac.end(),boost::false_type());
       
     this->stop();
   }
@@ -231,8 +231,8 @@ class Bench
    if (!fail){this->summarize(_pm.number_of_vertices(),_pm.number_of_halfedges());}
    
     
-    std::cout << "memory size after insert_curves()" << mem_sizer.virtual_size () << std::endl; 
-    std::cout << "memory resident size after insert_curves()" << mem_sizer.resident_size () << std::endl;
+    std::cout << "memory size after insert()" << mem_sizer.virtual_size () << std::endl; 
+    std::cout << "memory resident size after insert()" << mem_sizer.resident_size () << std::endl;
  }
  
 
diff --git a/Circular_kernel_2/Benchmarks/arrangement_traits/benchmarks_arrangement.cpp b/Circular_kernel_2/Benchmarks/arrangement_traits/benchmarks_arrangement.cpp
index 14f2f3819fc..10a44b21aa8 100644
--- a/Circular_kernel_2/Benchmarks/arrangement_traits/benchmarks_arrangement.cpp
+++ b/Circular_kernel_2/Benchmarks/arrangement_traits/benchmarks_arrangement.cpp
@@ -195,7 +195,7 @@ Bench bench(Htmlfilename,Texfilename,Dxffilename[i]);
 // //     for (typename ArcContainer::const_iterator it=ac.begin();
 // // 	 it != ac.end(); ++it) {
 // //       //insert(_pm,_pl,*it);
-// //       insert_curves(_pm,*it,_pl);
+// //       insert(_pm,*it,_pl);
 // //     };
 // //     bench.stop();
 // //     bench.summarize(_pm.number_of_vertices(),_pm.number_of_halfedges());
diff --git a/Circular_kernel_2/Benchmarks/benchmark.h b/Circular_kernel_2/Benchmarks/benchmark.h
index f3651efd872..ebc5e887648 100644
--- a/Circular_kernel_2/Benchmarks/benchmark.h
+++ b/Circular_kernel_2/Benchmarks/benchmark.h
@@ -29,13 +29,13 @@ private:
   int i;
 typedef std::size_t size_type;
   CGAL::Memory_sizer mem_sizer;
-  char* Dxffile;
+  std::string Dxffile;
   bool ONLY_DXF;
   double MemBefore,MemAfter;
   
 public:
   
-  Bench(const bool only_dxf=false, char *fhtml="benchmarks.html", char* ftex="benchmarks.tex",char* Dxffilename=""):
+  Bench(const bool only_dxf=false, const char *fhtml="benchmarks.html", const char* ftex="benchmarks.tex",const char* Dxffilename=""):
      htmlout(fhtml,std::ios::app),
      texout(ftex,std::ios::app){ 
 	i=0;
@@ -161,7 +161,7 @@ private:
 
   void summarize(int vertices,int hedges){
    	int temp; 
-   	temp=CGAL::Interval_nt<>::number_of_failures();	
+//   	temp=CGAL::Interval_nt<>::number_of_failures();	
    	numof_f_fails =  temp - numof_f_fails; 
    	std::cout  << "  numbers_of_filter_fails : " << numof_f_fails << std::endl;
    	
@@ -188,7 +188,7 @@ private:
 	      << "  Time (sec): " << utime.tv_sec << std::endl
 	      << "      (usec): " << std::setw(6) << std::setfill('0')
 	     			  << utime.tv_usec << std::endl;
-  	numof_f_fails = CGAL::Interval_nt<>::number_of_failures();
+//  	numof_f_fails = CGAL::Interval_nt<>::number_of_failures();
   }
   
   void fail(void){
@@ -213,13 +213,13 @@ private:
   	typedef typename CGAL::Arr_naive_point_location<Pmwx>        Point_location;
   	
 	std::cout << "memory size before construction" << mem_sizer.virtual_size() << std::endl;
-  	std::cout << "memory resident size before insert_curves()" << mem_sizer.resident_size () << std::endl;
+  	std::cout << "memory resident size before insert()" << mem_sizer.resident_size () << std::endl;
   	MemBefore = mem_sizer.virtual_size ()/1000000;
 	Pmwx _pm;
   	Point_location _pl(_pm);
 	try{
     		this->start(); 
-      		insert_curves(_pm,ac.begin(),ac.end());
+      		insert(_pm,ac.begin(),ac.end(),boost::false_type());
     		this->stop();
   	} catch (std::exception &e) {
     		this->fail();
@@ -236,8 +236,8 @@ private:
    
     	
         MemAfter = mem_sizer.virtual_size ()/1000000;
-	std::cout << "memory size after insert_curves()" << mem_sizer.virtual_size () << std::endl; 
-    	std::cout << "memory resident size after insert_curves()" << mem_sizer.resident_size () << std::endl;
+	std::cout << "memory size after insert()" << mem_sizer.virtual_size () << std::endl; 
+    	std::cout << "memory resident size after insert()" << mem_sizer.resident_size () << std::endl;
         _pm.clear();
  }
  
@@ -282,7 +282,7 @@ template <class CK,class Traits,class ArcContainer>
  }
 
  template <class CK,class Traits,class ArcContainer>
- void dfx(char* Dfxfile){
+ void dfx(const char* Dfxfile){
 	i=4;
  
       	ArcContainer arc;
@@ -316,7 +316,7 @@ template <class CK,class Traits,class ArcContainer>
  }
 public:
  template <class CK,class Traits,class ArcContainer>
- void Compute(char* dxffile){
+ void Compute(const char* dxffile){
      	if(!ONLY_DXF){
 	this->grid<CK,Traits,ArcContainer>();
    	this->grid2<CK,Traits,ArcContainer>();
@@ -351,12 +351,12 @@ public:
  }
 
 template <class CK,class Traits,class ArcContainer>
- void Compute_dxf(char* dxffile){
+ void Compute_dxf(const char* dxffile){
    	this->dfx<CK,Traits,ArcContainer>(dxffile);
    	this->close_row(); 
  }
 
- void kernel(char* kernel){ 
+ void kernel(const char* kernel){ 
 	this->open_row();
      	this->open_cell();
      	htmlout << kernel;
@@ -365,8 +365,8 @@ template <class CK,class Traits,class ArcContainer>
  }
 
  
- void newDxfFilename(char* Dxffilename=""){
-	char* newDxf = Dxffilename;
+ void newDxfFilename(const char* Dxffilename=""){
+	const char* newDxf = Dxffilename;
 	
      	if(!ONLY_DXF){
     		htmlout<< "<tr  bgcolor=\"gray\"><td>Kernel</td><td>grid I</td><td>grid II</td><td>random double</td><td>Dxf input is: "<< newDxf <<"</td><td> rotation </td></tr>" 
diff --git a/Circular_kernel_2/Benchmarks/benchmark_CK2.cpp b/Circular_kernel_2/Benchmarks/benchmark_CK2.cpp
index 199e1b78192..6860df8c89e 100644
--- a/Circular_kernel_2/Benchmarks/benchmark_CK2.cpp
+++ b/Circular_kernel_2/Benchmarks/benchmark_CK2.cpp
@@ -10,12 +10,12 @@
 #include <CGAL/Algebraic_kernel_for_circles_2_2.h>
 #include <CGAL/intersections.h>
 #include <CGAL/Circular_kernel_2.h>
-#include <CGAL/Arr_circular_arc_traits.h>
+#include <CGAL/Arr_circular_arc_traits_2.h>
 #include <CGAL/Lazy_circular_kernel_2.h>
 #include <CGAL/Filtered_bbox_circular_kernel_2.h>
 #include <CGAL/Arrangement_2.h>
 #include <CGAL/Arr_naive_point_location.h>
-#include <CGAL/Arr_circular_line_arc_traits.h>
+#include <CGAL/Arr_circular_line_arc_traits_2.h>
 #include <CGAL/Timer.h>
 #include <sys/time.h>
 #include <sys/resource.h>
@@ -23,19 +23,20 @@
 #include <fstream>
 #include <iomanip>
 
+#include <boost/type_traits.hpp>
+
 // CIRCULAR KERNEL TYPEDEFS
 typedef CGAL::MP_Float RT;
 typedef CGAL::Quotient<RT> NT1;
 typedef CGAL::Cartesian<NT1> Linear_k1;
 typedef CGAL::Algebraic_kernel_for_circles_2_2<NT1> Algebraic_k1;
 typedef CGAL::Circular_kernel_2<Linear_k1, Algebraic_k1> CircularKernel;
-typedef CGAL::Arr_circular_arc_traits<CircularKernel> CircularK_CA_Traits;
+typedef CGAL::Arr_circular_arc_traits_2<CircularKernel> CircularK_CA_Traits;
 typedef CircularKernel::Circular_arc_2 CircularKArc;
 typedef std::vector<CircularKArc> CircularKArcContainer;
 typedef CircularKernel::Circular_arc_2 Circular_arc_2;
 typedef CircularKernel::Line_arc_2 Line_arc_2;
-typedef CGAL::Arr_circular_line_arc_traits<CircularKernel,
-                  Line_arc_2,Circular_arc_2>   CircularK_Variant_Traits;
+typedef CGAL::Arr_circular_line_arc_traits_2<CircularKernel>   CircularK_Variant_Traits;
 typedef boost::variant< Circular_arc_2, Line_arc_2 > CircularKVarArc;
 typedef std::vector<CircularKVarArc> CircularKVarArcContainer; 
 
@@ -45,20 +46,20 @@ typedef CGAL::Cartesian<NT3> Linear_k3;
 typedef CGAL::Algebraic_kernel_for_circles_2_2<NT3> Algebraic_k3;
 typedef CGAL::Circular_kernel_2 <Linear_k3,Algebraic_k3> CK3_;
 typedef CGAL::Lazy_circular_kernel_2<CircularKernel,CK3_> LazyCurvedK;
-typedef CGAL::Arr_circular_arc_traits<LazyCurvedK> LazyCurvedK_CA_Traits;
+typedef CGAL::Arr_circular_arc_traits_2<LazyCurvedK> LazyCurvedK_CA_Traits;
 typedef LazyCurvedK::Circular_arc_2 LazyArc;
 typedef std::vector<LazyArc> LazyArcContainer;
 typedef LazyCurvedK::Circular_arc_2 Circular_arc_3;
 typedef LazyCurvedK::Line_arc_2 Line_arc_3; 
 typedef boost::variant<Circular_arc_3,Line_arc_3 > LazyVarArc;
 typedef std::vector<LazyVarArc> LazyVarContainer;
-typedef CGAL::Arr_circular_line_arc_traits<LazyCurvedK,
-         Line_arc_3,Circular_arc_3> LazyCurvedK_Variant_Traits;
+//~ typedef CGAL::Arr_circular_line_arc_traits_2<LazyCurvedK,Line_arc_3,Circular_arc_3> LazyCurvedK_Variant_Traits;
+typedef CGAL::Arr_circular_line_arc_traits_2<LazyCurvedK> LazyCurvedK_Variant_Traits;
 
 // BBOX TYPEDEFS
 typedef CGAL::Filtered_bbox_circular_kernel_2<CircularKernel>
   BBCircularKernel ;
-typedef CGAL::Arr_circular_arc_traits<BBCircularKernel>
+typedef CGAL::Arr_circular_arc_traits_2<BBCircularKernel>
   BBCircularKernel_CA_Traits;
 typedef BBCircularKernel::Circular_arc_2
   BBCircularKernelArc;
@@ -72,13 +73,12 @@ typedef boost::variant<Circular_arc_6,Line_arc_6 >
   BBCircVarArc;
 typedef std::vector<BBCircVarArc>
   BBCircVarContainer; 
-typedef CGAL::Arr_circular_line_arc_traits<BBCircularKernel,
-  Line_arc_6,Circular_arc_6>  BBCircVariantTraits; 
+typedef CGAL::Arr_circular_line_arc_traits_2<BBCircularKernel>  BBCircVariantTraits; 
 
 // BBOX(LAZY)
 typedef CGAL::Filtered_bbox_circular_kernel_2<LazyCurvedK>
   BBLazyKernel ;
-typedef CGAL::Arr_circular_arc_traits<BBLazyKernel>
+typedef CGAL::Arr_circular_arc_traits_2<BBLazyKernel>
   BBLazyKernel_CA_Traits;
 typedef BBLazyKernel::Circular_arc_2
   BBLazyKernelArc;
@@ -92,11 +92,10 @@ typedef boost::variant<Circular_arc_lazybb,Line_arc_lazybb >
   BBLazyVarArc;
 typedef std::vector<BBLazyVarArc>
   BBLazyVarContainer; 
-typedef CGAL::Arr_circular_line_arc_traits<BBLazyKernel,
-  Line_arc_lazybb,Circular_arc_lazybb>  BBLazyVariantTraits;
+typedef CGAL::Arr_circular_line_arc_traits_2<BBLazyKernel>  BBLazyVariantTraits;
 
 template <class CK,class Traits,class ArcContainer>
-void do_main(char *s) {
+void do_main(const char *s) {
 
   // TYPEDEFS	
   typedef typename CK::Circular_arc_2      C2;
@@ -120,7 +119,7 @@ void do_main(char *s) {
   struct rusage before, after;
   struct timeval utime, stime;
   getrusage(RUSAGE_SELF,&before);
-  insert_curves(_pm,ac.begin(),ac.end());
+  insert(_pm,ac.begin(),ac.end(),boost::false_type());
   getrusage(RUSAGE_SELF,&after);
   timersub(&(after.ru_utime),&(before.ru_utime),&utime);
   timersub(&(after.ru_stime),&(before.ru_stime),&stime);
@@ -157,7 +156,7 @@ void do_main(int k) {
   if(k == 0) {
     for(cx = 0.0; cx <= 10.0; cx += 0.5) {
       for(cy = 0.0; cy <= 10.0; cy += 0.5) {
-        ac.push_back(typename CK::Construct_circle_2()(Point_2(cx,cy),rft));
+        ac.push_back(typename CK::Circular_arc_2 ( typename CK::Circle_2(Point_2(cx,cy),rft) ) );
       }
     }
   }
@@ -166,14 +165,14 @@ void do_main(int k) {
   if(k == 1) {
     for(cx = 0.0; cx <= 0.2; cx += 0.01) {
       for(cy = 0.0; cy <= 0.2; cy += 0.01) {
-        ac.push_back(typename CK::Construct_circle_2()(Point_2(cx,cy),rft));
+        ac.push_back(typename CK::Circular_arc_2 ( typename CK::Circle_2(Point_2(cx,cy),rft) ));
       }
     }
   }
 
   // ONE CIRCLE
   if(k == 2) {
-    ac.push_back(typename CK::Construct_circle_2()(Point_2(0,0),5));
+    ac.push_back(typename CK::Circular_arc_2 ( typename CK::Circle_2(Point_2(0,0),5) ));
   }
 
   // RANDOM CASE
@@ -185,7 +184,7 @@ void do_main(int k) {
       double x = theRandom.get_double(0.0,1.0);
       double y = theRandom.get_double(0.0,1.0);
       double r = theRandom.get_double(0.00001,1.0);
-      ac.push_back(typename CK::Construct_circle_2()(Point_2(x,y),FT(r)));
+      ac.push_back(typename CK::Circular_arc_2 ( typename CK::Circle_2(Point_2(x,y),FT(r)) ));
     }
   }
   
@@ -194,10 +193,10 @@ void do_main(int k) {
     double h = (std::sqrt(3.0)+0.01);
     for(cx = 0.0; cx <= 40.4; cx += 2.01) {
       for(cy = h; cy <= h*20; cy += h*2) {
-        ac.push_back(typename CK::Construct_circle_2()(Point_2(cx+1.0,cy),rft));
+        ac.push_back(typename CK::Circular_arc_2 ( typename CK::Circle_2(Point_2(cx+1.0,cy),rft) ));
       }
       for(cy = 0.0; cy <= h*20.0; cy += h*2) {
-        ac.push_back(typename CK::Construct_circle_2()(Point_2(cx,cy),rft));
+        ac.push_back(typename CK::Circular_arc_2 ( typename CK::Circle_2(Point_2(cx,cy),rft)));
       }
     }
   }
@@ -210,7 +209,7 @@ void do_main(int k) {
   struct rusage before, after;
   struct timeval utime, stime;
   getrusage(RUSAGE_SELF,&before);
-  insert_curves(_pm,ac.begin(),ac.end());
+  insert(_pm,ac.begin(),ac.end(),boost::false_type());
   getrusage(RUSAGE_SELF,&after);
   timersub(&(after.ru_utime),&(before.ru_utime),&utime);
   timersub(&(after.ru_stime),&(before.ru_stime),&stime);
@@ -228,15 +227,15 @@ void do_main(int k) {
 
 int main(int argc, char* argv[]){
 
-  char* dxf_filename[] = { "DXF/51.dxf",
-                           "DXF/cad_l1.dxf",
-                           "DXF/cad_l2.dxf",
-                           "DXF/che_mod1.dxf",
-                           "DXF/CIOnZDraw.dxf",
-                           "DXF/mask1.dxf",
-                           "DXF/elekonta.dxf",
-                           "DXF/netlist_signal_1.dxf",
-                           "DXF/painttrack.dxf" };   	
+  const char* dxf_filename[] = { "DXF/51.dxf",
+                                 "DXF/cad_l1.dxf",
+                                 "DXF/cad_l2.dxf",
+                                 "DXF/che_mod1.dxf",
+                                 "DXF/CIOnZDraw.dxf",
+                                 "DXF/mask1.dxf",
+                                 "DXF/elekonta.dxf",
+                                 "DXF/netlist_signal_1.dxf",
+                                 "DXF/painttrack.dxf" };   	
   if(argc == 3) {
     int i = argv[1][0]-'0';
     int j = argv[2][0]-'0';
diff --git a/Circular_kernel_2/Benchmarks/benchmarks_arrangement.cpp b/Circular_kernel_2/Benchmarks/benchmarks_arrangement.cpp
index ee68ca4423d..8cd6298208e 100644
--- a/Circular_kernel_2/Benchmarks/benchmarks_arrangement.cpp
+++ b/Circular_kernel_2/Benchmarks/benchmarks_arrangement.cpp
@@ -18,18 +18,20 @@
 #include <CGAL/intersections.h>
 
 #include <CGAL/Circular_kernel_2.h>
-#include <CGAL/Arr_circular_arc_traits.h>
+#include <CGAL/Arr_circular_arc_traits_2.h>
 //#include <CGAL/Circular_arc_traits_tracer.h>
 
 #include <CGAL/Lazy_circular_kernel_2.h>
 
+#ifdef CIRCULAR_KERNEL_2_FILTERED_HEXAGON
 #include <CGAL/Filtered_hexagon_circular_kernel_2.h>
+#endif
 
 #include <CGAL/Filtered_bbox_circular_kernel_2.h>
 
 #include <CGAL/Arrangement_2.h>
 #include <CGAL/Arr_naive_point_location.h>
-#include <CGAL/Arr_circular_line_arc_traits.h>
+#include <CGAL/Arr_circular_line_arc_traits_2.h>
 
 
 #include <CGAL/Random.h>
@@ -39,9 +41,9 @@
 
 int main(int argc, char* argv[])
 {	//char* Dxffilename[]={"myFirst.dxf","cad_l1.dxf"};
-    char* Dxffilename[]={"myFirst.dxf","minimask0.dxf","minimask1.dxf","mask0.dxf","mask1.dxf","smallpainttrack.dxf","mask0_25.dxf","mask0_5.dxf","cad_l2.dxf","cad_l1.dxf","CIOnZDraw.dxf","che_mod1.dxf","elekonta.dxf","painttrack.dxf","netlist_signal_1.dxf","51.dxf"}; 
-    char* Htmlfilename;
-    char* Texfilename;
+    const char* Dxffilename[]={"myFirst.dxf","minimask0.dxf","minimask1.dxf","mask0.dxf","mask1.dxf","smallpainttrack.dxf","mask0_25.dxf","mask0_5.dxf","cad_l2.dxf","cad_l1.dxf","CIOnZDraw.dxf","che_mod1.dxf","elekonta.dxf","painttrack.dxf","netlist_signal_1.dxf","51.dxf"}; 
+    std::string Htmlfilename;
+    std::string Texfilename;
     char exten[4];
     int i;
     i=0;
@@ -154,7 +156,7 @@ Bench bench;			//If you want create table with all datasets you supose to use th
   typedef CGAL::Circular_kernel_2<Linear_k1, Algebraic_k1>     CircularKernel;
 
 //  #ifndef CGAL_CURVED_KERNEL_DEBUG
-  typedef CGAL::Arr_circular_arc_traits<CircularKernel> CircularK_CA_Traits;
+  typedef CGAL::Arr_circular_arc_traits_2<CircularKernel> CircularK_CA_Traits;
 //   #else
 //    typedef  CGAL::Circular_arc_traits<CircularKernel>          Traits0;
 //    typedef  CGAL::Circular_arc_traits_tracer<Traits0>          CircularK_CA_Traits;
@@ -169,7 +171,7 @@ Bench bench;			//If you want create table with all datasets you supose to use th
  
   typedef CircularKernel::Circular_arc_2                                  Circular_arc_2;
   typedef CircularKernel::Line_arc_2                                      Line_arc_2;
-  typedef CGAL::Arr_circular_line_arc_traits<CircularKernel,Line_arc_2,Circular_arc_2>  CircularK_Variant_Traits;
+  typedef CGAL::Arr_circular_line_arc_traits_2<CircularKernel>  CircularK_Variant_Traits;
  
   typedef boost::variant< Circular_arc_2, Line_arc_2 >        CircularKVarArc;
   typedef std::vector<CircularKVarArc>                        CircularKVarArcContainer; 
@@ -203,7 +205,7 @@ bench.Compute_no_dxf<CircularKernel,CircularK_Variant_Traits,CircularKVarArcCont
   typedef CGAL::Lazy_circular_kernel_2<CK2_,CK3_>                  LazyCurvedK;
   
 //   #ifndef CGAL_CURVED_KERNEL_DEBUG
-  typedef CGAL::Arr_circular_arc_traits<LazyCurvedK> LazyCurvedK_CA_Traits;
+  typedef CGAL::Arr_circular_arc_traits_2<LazyCurvedK> LazyCurvedK_CA_Traits;
 //    #else
 //    typedef  CGAL::Circular_arc_traits<LazyCurved_k>                 Traits0_2;
 //    typedef  CGAL::Circular_arc_traits_tracer<Traits0_2>         LazyCurved_kTraits;
@@ -221,7 +223,7 @@ bench.Compute_no_dxf<CircularKernel,CircularK_Variant_Traits,CircularKVarArcCont
   typedef LazyCurvedK::Line_arc_2  Line_arc_3; 
   typedef boost::variant<Circular_arc_3,Line_arc_3 >               LazyVarArc;
   typedef std::vector<LazyVarArc>                                  LazyVarContainer;
-  typedef CGAL::Arr_circular_line_arc_traits<LazyCurvedK,Line_arc_3,Circular_arc_3> LazyCurvedK_Variant_Traits;
+  typedef CGAL::Arr_circular_line_arc_traits_2<LazyCurvedK> LazyCurvedK_Variant_Traits;
   
   bench.kernel("LazyKVar");
   
@@ -239,7 +241,7 @@ bench.Compute_no_dxf<CircularKernel,CircularK_Variant_Traits,CircularKVarArcCont
   typedef CGAL::Filtered_hexagon_circular_kernel_2<CircularKernel>        CircularKernelHexagon;
  
 //   #ifndef CGAL_CURVED_KERNEL_DEBUG
-  typedef CGAL::Arr_circular_arc_traits<CircularKernelHexagon>                 CircularKernHex_CA_Traits;
+  typedef CGAL::Arr_circular_arc_traits_2<CircularKernelHexagon>                 CircularKernHex_CA_Traits;
 //   #else
 //   typedef CGAL::Circular_arc_traits<CircularKernelHexagon>                 Traits0_3;
 //   typedef CGAL::Circular_arc_traits_tracer<Traits0_3>     CircularKernHex_CA_Traits;
@@ -256,7 +258,7 @@ bench.Compute_no_dxf<CircularKernel,CircularK_Variant_Traits,CircularKVarArcCont
   typedef CircularKernelHexagon::Line_arc_2                                                       Line_arc_4;
   typedef boost::variant<  Circular_arc_4, Line_arc_4 >                          CircularKernHexVarArc;
   typedef std::vector<CircularKernHexVarArc>                                     CircularKernHexVarArcContainer; 
-  typedef CGAL::Arr_circular_line_arc_traits<CircularKernelHexagon,Circular_arc_4,Line_arc_4>  CircularKernHex_Variant_Traits;
+  typedef CGAL::Arr_circular_line_arc_traits_2<CircularKernelHexagon>  CircularKernHex_Variant_Traits;
   
   bench.kernel("CK Hex VarTraits");
  
@@ -275,7 +277,7 @@ bench.Compute_no_dxf<CircularKernel,CircularK_Variant_Traits,CircularKVarArcCont
   typedef CGAL::Filtered_hexagon_circular_kernel_2<LazyCurvedK>  LazyKernelHexagon;	
    
 //   #ifndef CGAL_CURVED_KERNEL_DEBUG
-  typedef CGAL::Arr_circular_arc_traits<LazyKernelHexagon>                  LazyKernelHexagon_CA_Traits;
+  typedef CGAL::Arr_circular_arc_traits_2<LazyKernelHexagon>                  LazyKernelHexagon_CA_Traits;
 //   #else
 //   typedef CGAL::Circular_arc_traits<LazyKernelHexagon>                  Traits0_4;
 //   typedef CGAL::Circular_arc_traits_tracer<Traits0_4>            LazyKernelHexagon_CA_Traits;
@@ -291,7 +293,7 @@ bench.Compute_no_dxf<CircularKernel,CircularK_Variant_Traits,CircularKVarArcCont
   typedef LazyKernelHexagon::Line_arc_2                                            Line_arc_5;
   typedef boost::variant<Circular_arc_5,Line_arc_5 >                  HxLazyVarArc;
   typedef std::vector<HxLazyVarArc>                                   HxLazyVarContainer;
-  typedef CGAL::Arr_circular_line_arc_traits<LazyKernelHexagon,Line_arc_5,Circular_arc_5>  HxLazyVariantTraits; 
+  typedef CGAL::Arr_circular_line_arc_traits_2<LazyKernelHexagon>  HxLazyVariantTraits; 
   
   bench.kernel("LazyK Hex  VarTraits") ;
 
@@ -308,7 +310,7 @@ bench.Compute_no_dxf<LazyKernelHexagon,HxLazyVariantTraits,HxLazyVarContainer>()
   typedef CGAL::Filtered_bbox_circular_kernel_2<CircularKernel>           BBCircularKernel ;
  
 //    #ifndef CGAL_CURVED_KERNEL_DEBUG
-  typedef CGAL::Arr_circular_arc_traits<BBCircularKernel>                  BBCircularKernel_CA_Traits;
+  typedef CGAL::Arr_circular_arc_traits_2<BBCircularKernel>                  BBCircularKernel_CA_Traits;
 //   #else
 //   typedef CGAL::Circular_arc_traits<BBCircularKernel>                  Traits0_5;
 //   typedef CGAL::Circular_arc_traits_tracer<Traits0_5>            BBCircularKernel_CA_Traits;
@@ -323,7 +325,7 @@ bench.Compute_no_dxf<LazyKernelHexagon,HxLazyVariantTraits,HxLazyVarContainer>()
   typedef BBCircularKernel::Line_arc_2                                            Line_arc_6;
   typedef boost::variant<Circular_arc_6,Line_arc_6 >                  BBCircVarArc;
   typedef std::vector<BBCircVarArc>                                   BBCircVarContainer;
-  typedef CGAL::Arr_circular_line_arc_traits<BBCircularKernel,Line_arc_6,Circular_arc_6>  BBCircVariantTraits; 
+  typedef CGAL::Arr_circular_line_arc_traits_2<BBCircularKernel>  BBCircVariantTraits; 
   
   bench.kernel("CK BBox VarTraits") ;
   
@@ -340,7 +342,7 @@ bench.Compute_no_dxf<LazyKernelHexagon,HxLazyVariantTraits,HxLazyVarContainer>()
    typedef CGAL::Filtered_bbox_circular_kernel_2<LazyCurvedK>              BBLazyCurvedK; 
   
 //    #ifndef CGAL_CURVED_KERNEL_DEBUG
-  typedef CGAL::Arr_circular_arc_traits<BBLazyCurvedK>                  BBLazyCurvedK_CA_Traits;
+  typedef CGAL::Arr_circular_arc_traits_2<BBLazyCurvedK>                  BBLazyCurvedK_CA_Traits;
 //   #else
 //   typedef CGAL::Circular_arc_traits<BBLazyCurvedK>                  Traits0_6;
 //   typedef CGAL::Circular_arc_traits_tracer<Traits0_6>            BBLazyCurvedK_CA_Traits;
@@ -357,7 +359,7 @@ bench.Compute_no_dxf<LazyKernelHexagon,HxLazyVariantTraits,HxLazyVarContainer>()
   typedef BBLazyCurvedK::Line_arc_2                                            Line_arc_7;
   typedef boost::variant<Circular_arc_7,Line_arc_7 >                  BBLazyVarArc;
   typedef std::vector< BBLazyVarArc>                                    BBLazyVarContainer;
-  typedef CGAL::Arr_circular_line_arc_traits<BBLazyCurvedK,Line_arc_7,Circular_arc_7>   BBLazyVariantTraits; 
+  typedef CGAL::Arr_circular_line_arc_traits_2<BBLazyCurvedK>   BBLazyVariantTraits; 
   
   bench.kernel("LLazyK BBox VarTraits") ;
   
diff --git a/Circular_kernel_2/Benchmarks/incremental_insertion/benchmark.h b/Circular_kernel_2/Benchmarks/incremental_insertion/benchmark.h
index 97629a2a126..2ab0bd868d0 100644
--- a/Circular_kernel_2/Benchmarks/incremental_insertion/benchmark.h
+++ b/Circular_kernel_2/Benchmarks/incremental_insertion/benchmark.h
@@ -208,7 +208,7 @@ class Bench
   typedef typename CGAL::Arrangement_2<Traits>                 Pmwx;
   typedef typename CGAL::Arr_naive_point_location<Pmwx>        Point_location;
   std::cout << "memory size before construction" << mem_sizer.virtual_size() << std::endl;
-  std::cout << "memory resident size before insert_curves()" << mem_sizer.resident_size () << std::endl;
+  std::cout << "memory resident size before insert()" << mem_sizer.resident_size () << std::endl;
   Pmwx _pm;
   Point_location _pl(_pm);
   
@@ -217,7 +217,7 @@ class Bench
     this->start();
     for (typename ArcContainer::const_iterator it=ac.begin();
 	 it != ac.end(); ++it) {
-      insert_curve(_pm,*it,_pl);
+      insert(_pm,*it,_pl,boost::false_type());
     };
     this->stop();
   }
@@ -234,8 +234,8 @@ class Bench
    if (!fail){this->summarize(_pm.number_of_vertices(),_pm.number_of_halfedges());}
    
     _pm.clear();
-    std::cout << "memory size after insert_curves()" << mem_sizer.virtual_size () << std::endl; 
-    std::cout << "memory resident size after insert_curves()" << mem_sizer.resident_size () << std::endl;
+    std::cout << "memory size after insert()" << mem_sizer.virtual_size () << std::endl; 
+    std::cout << "memory resident size after insert()" << mem_sizer.resident_size () << std::endl;
  }
  
 
diff --git a/Circular_kernel_2/Benchmarks/makefile b/Circular_kernel_2/Benchmarks/makefile
deleted file mode 100644
index 0747d1d22e6..00000000000
--- a/Circular_kernel_2/Benchmarks/makefile
+++ /dev/null
@@ -1,66 +0,0 @@
-# Created by the script cgal_create_makefile
-# This is the makefile for compiling a CGAL application.
-
-#---------------------------------------------------------------------#
-#                    include platform specific settings
-#---------------------------------------------------------------------#
-# Choose the right include file from the <cgalroot>/make directory.
-
-# CGAL_MAKEFILE = ENTER_YOUR_INCLUDE_MAKEFILE_HERE
-
-           #-DNDEBUG \
-           #-O2 -fprofile-arcs -ftest-coverage \
-           #-DCGAL_PROFILE \
-           #-g
-
-include $(CGAL_MAKEFILE)
-
-
-#---------------------------------------------------------------------#
-#                    compiler flags
-#---------------------------------------------------------------------#
-
-CXXFLAGS = \
-	   -DNDEBUG \
-	   -O2  \
-	   -I../include \
-           $(TESTSUITE_CXXFLAGS) \
-           $(EXTRA_FLAGS) \
-           $(CGAL_CXXFLAGS) \
-           $(LONG_NAME_PROBLEM_CXXFLAGS)
-
-#---------------------------------------------------------------------#
-#                    linker flags
-#---------------------------------------------------------------------#
-
-LIBPATH = \
-          $(CGAL_LIBPATH)
-
-LDFLAGS = \
-          $(LONG_NAME_PROBLEM_LDFLAGS) \
-          $(CGAL_LDFLAGS)
-#---------------------------------------------------------------------#
-#                    target entries
-#---------------------------------------------------------------------#
-
-all:            \
-                benchmark_CK2$(EXE_EXT)\
-                benchmarks_arrangement$(EXE_EXT) 
-
-benchmarks_arrangement$(EXE_EXT): benchmarks_arrangement$(OBJ_EXT)
-	$(CGAL_CXX) $(LIBPATH) $(EXE_OPT)benchmarks_arrangement benchmarks_arrangement$(OBJ_EXT) $(LDFLAGS)
-
-benchmark_CK2$(EXE_EXT): benchmark_CK2$(OBJ_EXT)
-	$(CGAL_CXX) $(LIBPATH) $(EXE_OPT)benchmark_CK2 benchmark_CK2$(OBJ_EXT) $(LDFLAGS)
-
-clean: \
-                   benchmarks_arrangement.clean\
-                   benchmark_CK2.clean 
-
-#---------------------------------------------------------------------#
-#                    suffix rules
-#---------------------------------------------------------------------#
-
-.cpp$(OBJ_EXT):
-	$(CGAL_CXX) $(CXXFLAGS) $(OBJ_OPT) $<
-
diff --git a/Circular_kernel_2/include/CGAL/Circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
index 48b3cd9487d..eaebb6f9114 100644
--- a/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Circular_kernel_2.h
@@ -93,7 +93,13 @@ struct Circular_kernel_2
         >,
        Circular_kernel_2<LinearKernel,AlgebraicKernel>
      >
-{};
+{
+  // for Lazy hexagons/bbox kernels
+  // Please remove this if you consider it to be sloppy
+  struct Circular_tag{};
+  typedef Circular_tag Definition_tag;
+  //  
+};
 
 } //namespace CGAL
 
diff --git a/Circular_kernel_2/include/CGAL/Filtered_hexagon_circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Filtered_hexagon_circular_kernel_2.h
index dd44c93bfbf..235e0e20298 100644
--- a/Circular_kernel_2/include/CGAL/Filtered_hexagon_circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Filtered_hexagon_circular_kernel_2.h
@@ -63,8 +63,8 @@ template <class CK>
     typedef typename CK::Compare_x_2                 Compare_x_2;
     typedef typename CK::Compare_y_2		     Compare_y_2;
     typedef typename CK::Compare_xy_2		     Compare_xy_2;
-    typedef typename CK::Compute_Circular_x_2        Compute_Circular_x_2;
-    typedef typename CK::Compute_Circular_y_2        Compute_Circular_y_2;
+    typedef typename CK::Compute_circular_x_2        Compute_circular_x_2;
+    typedef typename CK::Compute_circular_y_2        Compute_circular_y_2;
     typedef Hexagon_functors::Construct_circular_source_vertex_2<Self> Construct_circular_source_vertex_2;
     typedef Hexagon_functors::Construct_circular_target_vertex_2<Self> Construct_circular_target_vertex_2;
     typedef Hexagon_functors::Construct_circular_min_vertex_2<Self> Construct_circular_min_vertex_2;
diff --git a/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_2.h
index 42a7aa99882..f4129f036c0 100644
--- a/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_2.h
@@ -166,10 +166,6 @@ public:
                                      Lazy_make_x_monotone_2 <Kernel,typename AK::C, typename    EK::C>, \
             typename boost::mpl::if_<boost::is_same<typename AK::C, typename AK::Make_xy_monotone_2>, \
                                      Lazy_make_x_monotone_2 <Kernel,typename AK::C, typename    EK::C>, \
-            typename boost::mpl::if_<boost::is_same<typename AK::C, typename AK::Advanced_make_x_monotone_2>, \
-                                     Lazy_advanced_make_x_monotone_2 <Kernel,typename AK::C, typename    EK::C>, \
-            typename boost::mpl::if_<boost::is_same<typename AK::C, typename AK::Advanced_make_xy_monotone_2>, \
-                                     Lazy_advanced_make_x_monotone_2 <Kernel,typename AK::C, typename    EK::C>, \
 	    typename boost::mpl::if_<boost::is_same<typename AK::C, typename AK::Split_2>, \
                                      Lazy_functor_2_2 <Kernel, typename AK::C, typename EK::C>, \
             typename boost::mpl::if_<boost::is_same<typename AK::C::result_type, Bbox_2>, \
@@ -178,7 +174,7 @@ public:
                                      Lazy_construction_nt<Kernel,typename AK::C, typename EK::C>,\
             typename boost::mpl::if_<boost::is_same<typename AK::C::result_type, Object >,\
                                      Lazy_construction_object<Kernel,typename AK::C, typename EK::C>,\
-         Lazy_construction<Kernel,typename AK::C, typename EK::C> >::type >::type >::type >::type >::type >::type >::type >::type >::type C; \
+         Lazy_construction<Kernel,typename AK::C, typename EK::C> >::type >::type >::type >::type >::type >::type >::type C; \
     C Cf() const { return C(); }
 
 
diff --git a/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_constructions.h b/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_constructions.h
index c313ddacb82..8ef36266a26 100644
--- a/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_constructions.h
+++ b/Circular_kernel_2/include/CGAL/Lazy_circular_kernel_constructions.h
@@ -47,17 +47,17 @@ make_lazy_CK(const Object& eto)
            object_cast<std::pair<typename EK::Circular_arc_point_2,
 	                         unsigned > >(&eto))){
            return make_object(std::make_pair(typename LK::Circular_arc_point_2(
-	   new Lazy_construct_rep_0<typename AK::Circular_arc_point_2, 
+	   new Lazy_rep_0<typename AK::Circular_arc_point_2, 
 	   typename EK::Circular_arc_point_2, E2A>(ptr->first)),ptr->second));
   } else if(const typename EK::Circular_arc_2* ptr = 
             object_cast<typename EK::Circular_arc_2>(&eto)){
             return make_object(typename LK::Circular_arc_2(
-	    new Lazy_construct_rep_0<typename AK::Circular_arc_2, 
+	    new Lazy_rep_0<typename AK::Circular_arc_2, 
 	    typename EK::Circular_arc_2, E2A>(*ptr)));
   } else if(const typename EK::Line_arc_2* ptr = 
             object_cast<typename EK::Line_arc_2>(&eto)){
             return make_object(typename LK::Line_arc_2(
-	    new Lazy_construct_rep_0<typename AK::Line_arc_2, 
+	    new Lazy_rep_0<typename AK::Line_arc_2, 
 	    typename EK::Line_arc_2, E2A>(*ptr)));
   } else{
     std::cerr << "object_cast inside Lazy_construction_rep::operator() failed. It needs more else if's" << std::endl;
@@ -94,7 +94,7 @@ public:
     CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
     try {
       Protect_FPU_rounding<Protection> P;
-      Lazy_vector lv(new Lazy_construct_rep_with_vector_2<AC, EC, E2A, L1, L2>(ac, ec, l1, l2));
+      Lazy_vector lv(new Lazy_rep_with_vector_2<AC, EC, E2A, L1, L2>(ac, ec, l1, l2));
 
       for(unsigned int i = 0; i < lv.approx().size(); i++){
         
@@ -103,21 +103,21 @@ public:
 	if((temp_p=object_cast<std::pair<typename AK::Circular_arc_point_2,
 	                         unsigned > >(& (lv.approx()[i])))){
 	  *it = make_object(std::make_pair(typename LK::Circular_arc_point_2(
-	  new Lazy_construct_rep_1<Ith<typename AK::Circular_arc_point_2>, 
+	  new Lazy_rep_1<Ith<typename AK::Circular_arc_point_2>, 
 	  Ith<typename EK::Circular_arc_point_2>, E2A, 
 	  Lazy_vector>(Ith<typename AK::Circular_arc_point_2>(i,false), 
 	  Ith<typename EK::Circular_arc_point_2>(i,false), lv)),temp_p->second)); 
 	  ++it;
 	} else if(object_cast<typename AK::Circular_arc_2>(& (lv.approx()[i]))){
 	  *it = make_object(typename LK::Circular_arc_2(
-	  new Lazy_construct_rep_1<Ith<typename AK::Circular_arc_2>, 
+	  new Lazy_rep_1<Ith<typename AK::Circular_arc_2>, 
 	  Ith<typename EK::Circular_arc_2>,E2A, 
 	  Lazy_vector>(Ith<typename AK::Circular_arc_2>(i), 
 	  Ith<typename EK::Circular_arc_2>(i), lv)));
 	  ++it;
 	} else if(object_cast<typename AK::Line_arc_2>(& (lv.approx()[i]))){
 	  *it = make_object(typename LK::Line_arc_2(
-	  new Lazy_construct_rep_1<Ith<typename AK::Line_arc_2>, 
+	  new Lazy_rep_1<Ith<typename AK::Line_arc_2>, 
 	  Ith<typename EK::Line_arc_2>,E2A, 
 	  Lazy_vector>(Ith<typename AK::Line_arc_2>(i), 
 	  Ith<typename EK::Line_arc_2>(i), lv)));
@@ -172,20 +172,20 @@ public:
     CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
     try {
       Protect_FPU_rounding<Protection> P;
-      Lazy_vector lv(new Lazy_construct_rep_with_vector_1<AC, EC, E2A, L1>(ac, ec, l1));
+      Lazy_vector lv(new Lazy_rep_with_vector_1<AC, EC, E2A, L1>(ac, ec, l1));
       // lv.approx() is a std::vector<Object([AK::Point_2,AK::Segment_2])>
       // that is, when we get here we have constructed all approximate results
       for(unsigned int i = 0; i < lv.approx().size(); i++){
           if(object_cast<typename AK::Circular_arc_2>(& (lv.approx()[i]))){
 	  *it = make_object(typename LK::Circular_arc_2(
-	  new Lazy_construct_rep_1<Ith<typename AK::Circular_arc_2>, 
+	  new Lazy_rep_1<Ith<typename AK::Circular_arc_2>, 
 	  Ith<typename EK::Circular_arc_2>,E2A, 
 	  Lazy_vector>(Ith<typename AK::Circular_arc_2>(i), 
 	  Ith<typename EK::Circular_arc_2>(i), lv)));
 	  ++it;
 	} else if(object_cast<typename AK::Line_arc_2>(& (lv.approx()[i]))){
 	  *it = make_object(typename LK::Line_arc_2(
-	  new Lazy_construct_rep_1<Ith<typename AK::Line_arc_2>, 
+	  new Lazy_rep_1<Ith<typename AK::Line_arc_2>, 
 	  Ith<typename EK::Line_arc_2>,E2A, 
 	  Lazy_vector>(Ith<typename AK::Line_arc_2>(i), 
 	  Ith<typename EK::Line_arc_2>(i), lv)));
@@ -240,20 +240,20 @@ public:
     CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
     try {
       Protect_FPU_rounding<Protection> P;
-      Lazy_vector lv(new Lazy_construct_rep_with_vector_1<AC, EC, E2A, L1>(ac, ec, l1));
+      Lazy_vector lv(new Lazy_rep_with_vector_1<AC, EC, E2A, L1>(ac, ec, l1));
       // lv.approx() is a std::vector<Object([AK::Point_2,AK::Segment_2])>
       // that is, when we get here we have constructed all approximate results
       for(unsigned int i = 0; i < lv.approx().size(); i++){
           if(object_cast<typename AK::Circular_arc_2>(& (lv.approx()[i].first))){
 	  *it = std::make_pair(make_object(typename LK::Circular_arc_2(
-	  new Lazy_construct_rep_1<Ith<typename AK::Circular_arc_2>, 
+	  new Lazy_rep_1<Ith<typename AK::Circular_arc_2>, 
 	  Ith<typename EK::Circular_arc_2>,E2A, 
 	  Lazy_vector>(Ith<typename AK::Circular_arc_2>(i), 
 	  Ith<typename EK::Circular_arc_2>(i), lv))),lv.approx()[i].second);
 	  ++it;
 	} else if(object_cast<typename AK::Line_arc_2>(& (lv.approx()[i].first))){
 	  *it = std::make_pair(make_object(typename LK::Line_arc_2(
-	  new Lazy_construct_rep_1<Ith<typename AK::Line_arc_2>, 
+	  new Lazy_rep_1<Ith<typename AK::Line_arc_2>, 
 	  Ith<typename EK::Line_arc_2>,E2A, 
 	  Lazy_vector>(Ith<typename AK::Line_arc_2>(i), 
 	  Ith<typename EK::Line_arc_2>(i), lv))),lv.approx()[i].second);
@@ -315,30 +315,30 @@ template <typename L1>
     CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
     try {
       Protect_FPU_rounding<Protection> P;
-      Lazy_object lo(new Lazy_construct_rep_1<AC, EC, E2A, L1>(ac, ec, l1));
+      Lazy_object lo(new Lazy_rep_1<AC, EC, E2A, L1>(ac, ec, l1));
       
        std::pair<typename AK::Circular_arc_point_2, unsigned> *temp_p;
  
          if((temp_p=object_cast<std::pair<typename AK::Circular_arc_point_2, unsigned > >(& (lo.approx())))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
 	        Object_cast<typename EK::Circular_arc_point_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Circular_arc_point_2>(), 
 	        Object_cast<typename EK::Circular_arc_point_2>(), lo); 
 	        return make_object(std::make_pair(typename LK::Circular_arc_point_2(lcr),temp_p->second));
       } else if(object_cast<typename AK::Circular_arc_point_2>(& (lo.approx()))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
 	        Object_cast<typename EK::Circular_arc_point_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Circular_arc_point_2>(), 
 	        Object_cast<typename EK::Circular_arc_point_2>(), lo); 
 	        return make_object(typename LK::Circular_arc_point_2(lcr));
       } else if(object_cast<typename AK::Circular_arc_2>(& (lo.approx()))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Circular_arc_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Circular_arc_2>, 
 	        Object_cast<typename EK::Circular_arc_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Circular_arc_2>(), 
 		Object_cast<typename EK::Circular_arc_2>(), lo); 
 	        return make_object(typename LK::Circular_arc_2(lcr));}
 	else if(object_cast<typename AK::Line_arc_2>(& (lo.approx()))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Line_arc_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Line_arc_2>, 
 	        Object_cast<typename EK::Line_arc_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Line_arc_2>(), 
 		Object_cast<typename EK::Line_arc_2>(), lo); 
@@ -364,31 +364,31 @@ template <typename L1>
     CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
     try {
       Protect_FPU_rounding<Protection> P;
-      Lazy_object lo(new Lazy_construct_rep_2<AC, EC, E2A, L1, L2>(ac, ec, l1, l2));
+      Lazy_object lo(new Lazy_rep_2<AC, EC, E2A, L1, L2>(ac, ec, l1, l2));
  
       std::pair<typename AK::Circular_arc_point_2, unsigned> *temp_p;    
       
       
     if((temp_p=object_cast<std::pair<typename AK::Circular_arc_point_2, unsigned > >(& (lo.approx())))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
 	        Object_cast<typename EK::Circular_arc_point_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Circular_arc_point_2>(), 
 	        Object_cast<typename EK::Circular_arc_point_2>(), lo); 
 	        return make_object(std::make_pair(typename LK::Circular_arc_point_2(lcr),temp_p->second));
       } else if(object_cast<typename AK::Circular_arc_point_2>(& (lo.approx()))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Circular_arc_point_2>, 
 	        Object_cast<typename EK::Circular_arc_point_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Circular_arc_point_2>(), 
 	        Object_cast<typename EK::Circular_arc_point_2>(), lo); 
 	        return make_object(typename LK::Circular_arc_point_2(lcr));
       } else if(object_cast<typename AK::Circular_arc_2>(& (lo.approx()))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Circular_arc_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Circular_arc_2>, 
 	        Object_cast<typename EK::Circular_arc_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Circular_arc_2>(), 
 		Object_cast<typename EK::Circular_arc_2>(), lo); 
 	        return make_object(typename LK::Circular_arc_2(lcr));}
 	else if(object_cast<typename AK::Line_arc_2>(& (lo.approx()))){
-	typedef Lazy_construct_rep_1<Object_cast<typename AK::Line_arc_2>, 
+	typedef Lazy_rep_1<Object_cast<typename AK::Line_arc_2>, 
 	        Object_cast<typename EK::Line_arc_2>, E2A, Lazy_object> Lcr;
 	        Lcr * lcr = new Lcr(Object_cast<typename AK::Line_arc_2>(), 
 		Object_cast<typename EK::Line_arc_2>(), lo); 
diff --git a/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h b/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
index 129721d4090..389a1dc5e61 100644
--- a/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
+++ b/Circular_kernel_2/include/CGAL/Simple_circular_kernel_2.h
@@ -90,7 +90,13 @@ struct Circular_kernel_2
   >,
   Circular_kernel_2<LinearKernel,AlgebraicKernel>
   >
-{};
+{
+  // for Lazy hexagons/bbox kernels
+  // Please remove this if you consider it to be sloppy
+  struct Circular_tag{};
+  typedef Circular_tag Definition_tag;
+  //  
+};
 
 } //namespace CGAL