diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2.h
index aa262e81e8c..744ea488699 100644
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2.h
+++ b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2.h
@@ -23,7 +23,7 @@
 #ifndef CGAL_APOLLONIUS_GRAPH_2_H
 #define CGAL_APOLLONIUS_GRAPH_2_H
 
-//#define CGAL_APOLLONIUS_GRAPH_IS_HIDDEN_THREE_ARGUMENTS 1
+#define CGAL_APOLLONIUS_GRAPH_PSEUDO_CIRCLE_DESIGN 1
 
 
 #include <iostream>
@@ -775,28 +775,10 @@ public:
   }
 
 protected:
-  typedef Boolean_tag<Geom_traits::Is_hidden_2::Has_three_argument_operator>
-  Hidden_predicate_tag;
   // wrappers for the geometric predicates
 
   // checks is q is contained inside p
-  bool is_hidden(const Site_2 &p,
-		 const Site_2 &q) const;
-
-  // returns true if q is hidden by the sites p1 and p2
-  inline
-  bool is_hidden(const Site_2 &p1, const Site_2 &p2,
-		 const Site_2 &q, Tag_false) const
-  {
-    return false;
-  }
-
-  inline  
-  bool is_hidden(const Site_2 &p1, const Site_2 &p2,
-		 const Site_2 &q, Tag_true) const
-  {
-    return geom_traits().is_hidden_2_object()(p1, p2, q);
-  }
+  bool is_hidden(const Site_2 &p, const Site_2 &q) const;
 
   // returns:
   //   ON_POSITIVE_SIDE if q is closer to p1
diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Apollonius_graph_2_impl.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Apollonius_graph_2_impl.h
index 6cd01506a12..c15ff52d769 100644
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Apollonius_graph_2_impl.h
+++ b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Apollonius_graph_2_impl.h
@@ -490,29 +490,6 @@ insert_third(const Site_2& p)
     return v1;
   }
 
-#ifdef CGAL_APOLLONIUS_GRAPH_IS_HIDDEN_THREE_ARGUMENTS
-  if ( Geom_traits::Is_hidden_2::Has_three_argument_operator ) {
-    if ( is_hidden(v1->site(), v2->site(), p, Hidden_predicate_tag()) ) {
-      // p is hidden by both v1 and v2
-      v1->add_hidden_site(p);
-      v2->add_hidden_site(p);
-      return Vertex_handle();
-    } else if ( is_hidden(p, v1->site(), v2->site(), Hidden_predicate_tag()) ) {
-      // v2 is hidden by both v1 and p
-      v1->add_hidden_site(v2->site());
-      v2->add_hidden_site(v2->site());
-      v2->set_site(p);
-      return v2;
-    } else if ( is_hidden(v2->site(), p, v1->site(), Hidden_predicate_tag()) ) {
-      // v1 is hidden by both v2 and p
-      v1->add_hidden_site(v1->site());
-      v2->add_hidden_site(v1->site());
-      v1->set_site(p);
-      return v1;
-    }
-  }
-#endif
-
   Conflict_type ct =
     finite_edge_conflict_type_degenerated(v1->site(), v2->site(), p);
 
@@ -524,7 +501,6 @@ insert_third(const Site_2& p)
   }
 
 
-#ifndef CGAL_APOLLONIUS_GRAPH_IS_HIDDEN_THREE_ARGUMENTS
   Conflict_type ct1 =
     finite_edge_conflict_type_degenerated(v1->site(), p, v2->site());
 
@@ -534,7 +510,7 @@ insert_third(const Site_2& p)
   if ( ct == NO_CONFLICT && ct1 == NO_CONFLICT && ct2 == NO_CONFLICT ) {
     return Vertex_handle();
   }
-#endif
+
 
   Vertex_handle v = this->_tds.insert_dim_up(infinite_vertex());
   v->set_site(p);
@@ -573,11 +549,6 @@ insert_third(const Site_2& p)
     }
   } else {
     CGAL_assertion( ct == BOTH_VERTICES );
-#ifdef CGAL_APOLLONIUS_GRAPH_IS_HIDDEN_THREE_ARGUMENTS
-    Conflict_type ct1 =
-      finite_edge_conflict_type_degenerated(v1->site(), p, v2->site());
-#endif
-
     Edge_circulator ec =
       ( ct1 == INTERIOR ) ? incident_edges(v2) : incident_edges(v1);
     while ( true ) {
@@ -652,32 +623,15 @@ insert(const Site_2& p, Vertex_handle vnear)
     do {
       e = *ec;
 
-#ifdef CGAL_APOLLONIUS_GRAPH_IS_HIDDEN_THREE_ARGUMENTS 
-      if ( Geom_traits::Is_hidden_2::Has_three_argument_operator ) {
-	Vertex_handle v1( e.first->vertex(ccw(e.second)) );
-	Vertex_handle v2( e.first->vertex( cw(e.second)) );
-	if ( !is_infinite(v1) && !is_infinite(v2) &&
-	     is_hidden(v1->site(), v2->site(), p, Hidden_predicate_tag()) ) {
-	  v1->add_hidden_site(p);
-	  v2->add_hidden_site(p);
-	  return Vertex_handle();
-	}
-      }
-#endif
-
       interior_in_conflict = edge_interior(e, p, false);
 
       if ( interior_in_conflict ) { break; }
       ++ec;
     } while ( ec != ec_start );
 
-#ifdef CGAL_APOLLONIUS_GRAPH_IS_HIDDEN_THREE_ARGUMENTS
     if ( !interior_in_conflict ) {
       return Vertex_handle();
     }
-#else
-    CGAL_assertion( interior_in_conflict );
-#endif
 
     return insert_degree_2(e, p);
   }
diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Is_hidden_C2.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Is_hidden_C2.h
index ed4bc028485..ecdcdab5c7a 100644
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Is_hidden_C2.h
+++ b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Is_hidden_C2.h
@@ -72,8 +72,6 @@ public:
   typedef bool                 result_type;
   typedef Site_2               argument_type;
 
-  enum { Has_three_argument_operator = false };
-
   inline bool operator()(const Site_2 &p, const Site_2 &q) const {
 #ifdef AG2_PROFILE_PREDICATES
     ag2_predicate_profiler::is_trivial_counter++;
diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_filtered_traits_2.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_filtered_traits_2.h
index e5661c872fa..ad15b023e6a 100644
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_filtered_traits_2.h
+++ b/Apollonius_graph_2/include/CGAL/Apollonius_graph_filtered_traits_2.h
@@ -289,14 +289,9 @@ public:
   Orientation_2;
 
 
-  struct Is_hidden_2
-    : public Filtered_predicate<EK_Is_hidden_2, FK_Is_hidden_2, C2E, C2F>
-  {
-    enum {
-      Has_three_argument_operator =
-      EK_Is_hidden_2::Has_three_argument_operator
-    };
-  };
+  typedef
+  Filtered_predicate<EK_Is_hidden_2, FK_Is_hidden_2, C2E, C2F>
+  Is_hidden_2;
 
   typedef
   Filtered_predicate<EK_Oriented_side_of_bisector_2,