diff --git a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
index f3d854aa264..22c6da361a3 100644
--- a/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
+++ b/Periodic_3_triangulation_3/include/CGAL/Periodic_3_triangulation_3.h
@@ -3920,19 +3920,19 @@ namespace internal {
 
   /// Internal function used by operator==.
   // This function tests and registers the 4 neighbors of c1/c2,
-  // and recursively calls itself over them.
+  // and performs a bfs traversal
   // Returns false if an inequality has been found.
   //TODO: introduce offsets
   template <class GT, class TDS1, class TDS2>
   bool
   test_next(const Periodic_3_triangulation_3<GT, TDS1> &t1,
-      const Periodic_3_triangulation_3<GT, TDS2> &t2,
-      typename Periodic_3_triangulation_3<GT, TDS1>::Cell_handle c1,
-      typename Periodic_3_triangulation_3<GT, TDS2>::Cell_handle c2,
-      std::map<typename Periodic_3_triangulation_3<GT, TDS1>::Cell_handle,
-          typename Periodic_3_triangulation_3<GT, TDS2>::Cell_handle> &Cmap,
-      std::map<typename Periodic_3_triangulation_3<GT, TDS1>::Vertex_handle,
-          typename Periodic_3_triangulation_3<GT, TDS2>::Vertex_handle> &Vmap)
+            const Periodic_3_triangulation_3<GT, TDS2> & /* needed_for_deducing_TDS2 */,
+            typename Periodic_3_triangulation_3<GT, TDS1>::Cell_handle c1,
+            typename Periodic_3_triangulation_3<GT, TDS2>::Cell_handle c2,
+            std::map<typename Periodic_3_triangulation_3<GT, TDS1>::Cell_handle,
+            typename Periodic_3_triangulation_3<GT, TDS2>::Cell_handle> &Cmap,
+            std::map<typename Periodic_3_triangulation_3<GT, TDS1>::Vertex_handle,
+            typename Periodic_3_triangulation_3<GT, TDS2>::Vertex_handle> &Vmap)
   {  
     typedef Periodic_3_triangulation_3<GT, TDS1> Tr1;
     typedef Periodic_3_triangulation_3<GT, TDS2> Tr2;
@@ -3993,7 +3993,6 @@ namespace internal {
         
         // We register n1/n2.
         Cmap.insert(std::make_pair(n1, n2));
-        // We recurse on n1/n2.
         queue.push_back(std::make_pair(n1, n2));
       }
     }
@@ -4123,9 +4122,8 @@ operator==(const Periodic_3_triangulation_3<GT,TDS1> &t1,
   if (Cmap.size() == 0)
     return false;
 
-  // We now have one cell, we need to propagate recursively.
-  return internal::test_next(t1, t2,
-      Cmap.begin()->first, Cmap.begin()->second, Cmap, Vmap);
+  // We now have one cell, we need to compare in a bfs graph traversal
+  return internal::test_next(t1, t2, Cmap.begin()->first, Cmap.begin()->second, Cmap, Vmap);
 }
 
 template < class GT, class TDS1, class TDS2 >
diff --git a/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_3.h b/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_3.h
index db0096a558b..8298000de59 100644
--- a/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_3.h
+++ b/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_3.h
@@ -95,19 +95,16 @@ void test_periodic_3_triangulation_traits_3()
   std::cout<<"  GMP not available"<<std::endl;
 #endif
 
+#ifdef TEST_CARTESIAN
 #ifdef CGAL_USE_LEDA
   std::cout<<"  LEDA...";std::cout.flush();
 #define RT leda_integer
 #define FT leda_rational
   test_traits<KERNEL>();
-#define LRT CGAL::Lazy_exact_nt< RT >
-#define LFT CGAL::Lazy_exact_nt< FT >
-  test_traits<LAZY_KERNEL>();
+
   std::cout<<" done"<<std::endl;
 #undef RT
 #undef FT
-#undef LRT
-#undef LFT
 #else
   std::cout<<"  LEDA not available"<<std::endl;
 #endif
@@ -117,19 +114,13 @@ void test_periodic_3_triangulation_traits_3()
 #define RT CORE::Expr
 #define FT CGAL::Quotient<RT>
   test_traits<KERNEL>();
-#ifndef _MSC_VER
-#define LRT CGAL::Lazy_exact_nt< RT >
-#define LFT CGAL::Lazy_exact_nt< FT >
-  test_traits<LAZY_KERNEL>();
-#else
-  std::cout << "Skip test with Lazy_exact_nt<CORE::Expr>" << std::endl;
-#endif
+
   std::cout<<" done"<<std::endl;
 #undef RT
 #undef FT
-#undef LRT
-#undef LFT
 #else
   std::cout<<"  CORE not available"<<std::endl;
 #endif
+
+#endif
 }
diff --git a/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_C_3.cpp b/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_C_3.cpp
index ebc8583207f..1d64bab024d 100644
--- a/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_C_3.cpp
+++ b/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_C_3.cpp
@@ -19,6 +19,7 @@
 //
 // Author(s)     : Manuel Caroli <Manuel.Caroli@sophia.inria.fr>
 
+#define TEST_CARTESIAN 1
 #define KERNEL CGAL::Cartesian< FT > 
 #define LAZY_KERNEL CGAL::Cartesian< LFT > 
 
diff --git a/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_SC_3.cpp b/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_SC_3.cpp
index febba52e58e..78d16dc679e 100644
--- a/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_SC_3.cpp
+++ b/Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_SC_3.cpp
@@ -19,6 +19,7 @@
 //
 // Author(s)     : Manuel Caroli <Manuel.Caroli@sophia.inria.fr>
 
+#define TEST_CARTESIAN 1
 #define KERNEL CGAL::Simple_cartesian< FT > 
 #define LAZY_KERNEL CGAL::Simple_cartesian< LFT >