diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/comparator_profiler.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/comparator_profiler.h
index 968681f5128..e2ddc96f518 100644
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/comparator_profiler.h
+++ b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/comparator_profiler.h
@@ -24,6 +24,7 @@
 #define CGAL_COMPARATOR_PROFILER_H
 
 #include <CGAL/Apollonius_graph_2/basic.h>
+#include <CGAL/atomic.h>
 
 namespace CGAL {
 
@@ -32,23 +33,31 @@ namespace ApolloniusGraph_2 {
 class comparator_profiler
 {
 public:
-  static bool count_cases;
-  static unsigned long case_1_counter;
-  static unsigned long case_2_counter;
-  static unsigned long case_3a_Jpos_counter;
-  static unsigned long case_3a_Jneg_counter;
-  static unsigned long case_3b_Jpos_counter;
-  static unsigned long case_3b_Jneg_counter;
-  static unsigned long case_4_counter;
-  static unsigned long case_5_counter;
-  static unsigned long case_degenerate_counter;
+
+#ifdef CGAL_NO_ATOMIC
+  typedef bool bool_;
+  typedef unsigned long long_;
+#else
+  typedef CGAL::cpp11::atomic<bool> bool_;
+  typedef CGAL::cpp11::atomic<unsigned long> long_;
+#endif
+
+  static bool_ count_cases;
+  static long_ case_1_counter;
+  static long_ case_2_counter;
+  static long_ case_3a_Jpos_counter;
+  static long_ case_3a_Jneg_counter;
+  static long_ case_3b_Jpos_counter;
+  static long_ case_3b_Jneg_counter;
+  static long_ case_4_counter;
+  static long_ case_5_counter;
+  static long_ case_degenerate_counter;
 public:
-  static unsigned long counter_rr;
-  static unsigned long counter_rr_p3inf;
-  static unsigned long counter_rr_p4;
-  static unsigned long counter_rr_e;
-  static unsigned long counter_rr_r0;
-  //  static unsigned long counter_rr_jneg;
+  static long_ counter_rr;
+  static long_ counter_rr_p3inf;
+  static long_ counter_rr_p4;
+  static long_ counter_rr_e;
+  static long_ counter_rr_r0;
 
   static void reset()
   {
@@ -68,7 +77,6 @@ public:
     counter_rr_p4 = 0;
     counter_rr_e = 0;
     counter_rr_r0 = 0;
-    //    counter_rr_jneg = 0;
   }
 
   template< class FT >
@@ -141,6 +149,8 @@ public:
   }
 };
 
+#ifdef CGAL_NO_ATOMIC
+
 bool comparator_profiler::count_cases = false;
 unsigned long comparator_profiler::case_1_counter = 0;
 unsigned long comparator_profiler::case_2_counter = 0;
@@ -157,7 +167,9 @@ unsigned long comparator_profiler::counter_rr_p3inf = 0;
 unsigned long comparator_profiler::counter_rr_p4 = 0;
 unsigned long comparator_profiler::counter_rr_e = 0;
 unsigned long comparator_profiler::counter_rr_r0 = 0;
-//unsigned long comparator_profiler::counter_rr_jneg = 0;
+
+#endif
+
 
 } //namespace ApolloniusGraph_2
 
diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/predicate_profiler.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/predicate_profiler.h
index 703e38303e0..d9edf9bc76f 100644
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/predicate_profiler.h
+++ b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/predicate_profiler.h
@@ -24,6 +24,7 @@
 #define CGAL_APOLLONIUS_GRAPH_2_PREDICATE_PROFILER 1
 
 #include <CGAL/Apollonius_graph_2/basic.h>
+#include <CGAL/atomic.h>
 
 #define AG2_PROFILE_PREDICATES
 
@@ -34,18 +35,24 @@ namespace ApolloniusGraph_2 {
 class ag2_predicate_profiler
 {
 public:
+#ifdef CGAL_NO_ATOMIC
+  typedef unsigned long long_;
+#else
+  typedef CGAL::cpp11::atomic<unsigned long> long_;
+#endif
+
   // high level predicates
-  static unsigned long side_of_bisector_counter;
-  static unsigned long is_trivial_counter;
-  static unsigned long infinite_edge_conflict_type_counter;
-  static unsigned long finite_edge_conflict_type_counter;
+  static long_ side_of_bisector_counter;
+  static long_ is_trivial_counter;
+  static long_ infinite_edge_conflict_type_counter;
+  static long_ finite_edge_conflict_type_counter;
 
   // subpredicates
-  static unsigned long inside_circular_arc_counter;
-  static unsigned long distance_from_bitangent_counter;
-  static unsigned long shadow_region_type_counter;
-  static unsigned long incircle_counter;
-  static unsigned long order_on_bisector_counter;
+  static long_ inside_circular_arc_counter;
+  static long_ distance_from_bitangent_counter;
+  static long_ shadow_region_type_counter;
+  static long_ incircle_counter;
+  static long_ order_on_bisector_counter;
 
   static void reset() {
     side_of_bisector_counter = 0;
@@ -61,6 +68,9 @@ public:
   }
 };
 
+
+#ifdef CGAL_NO_ATOMIC
+
 unsigned long ag2_predicate_profiler::side_of_bisector_counter = 0;
 unsigned long ag2_predicate_profiler::is_trivial_counter = 0;
 unsigned long ag2_predicate_profiler::infinite_edge_conflict_type_counter = 0;
@@ -72,6 +82,8 @@ unsigned long ag2_predicate_profiler::shadow_region_type_counter = 0;
 unsigned long ag2_predicate_profiler::incircle_counter = 0;
 unsigned long ag2_predicate_profiler::order_on_bisector_counter = 0;
 
+#endif
+
 } //namespace ApolloniusGraph_2
 
 } //namespace CGAL
diff --git a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/uncertain/Uncertain_vertex_conflict_2.h b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/uncertain/Uncertain_vertex_conflict_2.h
index b37a11ac1a7..d941752077c 100644
--- a/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/uncertain/Uncertain_vertex_conflict_2.h
+++ b/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/uncertain/Uncertain_vertex_conflict_2.h
@@ -47,7 +47,7 @@ private:
     inline
     Uncertain<bool> is_less (const Site_2 &p0, const Site_2 &p1) const
     {
-      static Uncertain<bool> uncertain_bool =
+      static const Uncertain<bool> uncertain_bool =
 	Uncertain<bool>::indeterminate();
 
       Uncertain<Comparison_result> cr;
diff --git a/Apollonius_graph_2/include/CGAL/Hyperbola_ray_2.h b/Apollonius_graph_2/include/CGAL/Hyperbola_ray_2.h
index a8b03bd1ee0..bc3734eddc9 100644
--- a/Apollonius_graph_2/include/CGAL/Hyperbola_ray_2.h
+++ b/Apollonius_graph_2/include/CGAL/Hyperbola_ray_2.h
@@ -59,7 +59,7 @@ protected:
 #else
   static const FT& OFFSET()
   {
-    static FT offset_(10000);
+    static const FT offset_(10000);
     return offset_;
   }
 #endif
diff --git a/Apollonius_graph_2/include/CGAL/Parabola_2.h b/Apollonius_graph_2/include/CGAL/Parabola_2.h
index bc8bf874a74..ed804ab7fbb 100644
--- a/Apollonius_graph_2/include/CGAL/Parabola_2.h
+++ b/Apollonius_graph_2/include/CGAL/Parabola_2.h
@@ -48,21 +48,6 @@ public:
 private:
     typedef Algebraic_structure_traits<FT> AST;
 protected:
-  // static stuff
-#if defined(__POWERPC__) && \
-  defined(__GNUC__) && (__GNUC__ == 3) && (__GNUC_MINOR__ == 4)
-  // hack to avoid nasty warning for G++ 3.4 on Darwin
-  static FT STEP()
-  {
-    return FT(2);
-  }
-#else
-  static const FT& STEP()
-  {
-    static FT step_(2);
-    return step_;
-  }
-#endif
 
   //  inline static
   //  FT square(const FT &x)
@@ -291,9 +276,9 @@ public:
 
     pleft.push_back(o);
     pright.push_back(o);
-
+    const FT STEP(2);
     for (int i = 1; i <= 100; i++) {
-      p = compute_points(i * i * STEP());
+      p = compute_points(i * i * STEP);
 
       W << p[0];
       W << p[1];
diff --git a/Apollonius_graph_2/include/CGAL/Parabola_segment_2.h b/Apollonius_graph_2/include/CGAL/Parabola_segment_2.h
index d934341e700..bff8535a565 100644
--- a/Apollonius_graph_2/include/CGAL/Parabola_segment_2.h
+++ b/Apollonius_graph_2/include/CGAL/Parabola_segment_2.h
@@ -68,12 +68,12 @@ public:
   }
 
   int compute_k(const FT& tt) const {
-    //    return int(CGAL::to_double(CGAL::sqrt(tt / this->STEP())));
-    return int(CGAL::sqrt(CGAL::to_double(tt) / CGAL::to_double(this->STEP())));
+    return int(CGAL::sqrt(CGAL::to_double(tt) / 2));
   }
 
   void generate_points(std::vector<Point_2>& p) const
   {
+    const FT STEP(2);
     FT s0, s1;
 
     s0 = t(p1);
@@ -92,20 +92,21 @@ public:
 
       p.push_back( this->o );
       k = -1;
-      tt = -this->STEP();
+
+      tt = - STEP;
       while ( CGAL::compare(tt, s0) == LARGER ) {
 	p.insert( p.begin(), f(tt) );
 	k--;
-	tt = -FT(k * k) * this->STEP();
+	tt = -FT(k * k) * STEP;
       }
       p.insert( p.begin(), f(s0) );
 
       k = 1;
-      tt = this->STEP();
+      tt = STEP;
       while ( CGAL::compare(tt, s1) == SMALLER ) {
 	p.push_back( f(tt) );
 	k++;
-	tt = FT(k * k) * this->STEP();
+	tt = FT(k * k) * STEP;
       }
       p.push_back( f(s1) );
     } else if ( !(CGAL::is_negative(s0)) &&
@@ -123,7 +124,7 @@ public:
 	if ( CGAL::compare(tt, s0) != SMALLER )
 	  p.push_back( f(tt) );
 	k++;
-	tt = FT(k * k) * this->STEP();
+	tt = FT(k * k) * STEP;
       }
       p.push_back( f(s1) );
     } else {
@@ -139,7 +140,7 @@ public:
 	if ( CGAL::compare(tt, s1) != LARGER )
 	  p.push_back( f(tt) );
 	k--;
-	tt = -FT(k * k) * this->STEP();
+	tt = -FT(k * k) * STEP;
       }
       p.push_back( f(s0) );
     }
diff --git a/Apollonius_graph_2/include/CGAL/in_place_edge_list.h b/Apollonius_graph_2/include/CGAL/in_place_edge_list.h
index 0592aba5e1c..df5e8a6e1bd 100644
--- a/Apollonius_graph_2/include/CGAL/in_place_edge_list.h
+++ b/Apollonius_graph_2/include/CGAL/in_place_edge_list.h
@@ -164,7 +164,7 @@ public:
 
   void remove(const Edge& e) {
     CGAL_precondition( is_in_list(e) );
-    static Edge SENTINEL_QUEUE_EDGE = Edge(Face_handle(), -1);
+    static const Edge SENTINEL_QUEUE_EDGE = Edge(Face_handle(), -1);
 
     if ( is_singleton() ) {
       _front = SENTINEL_QUEUE_EDGE;