diff --git a/Mesh_3/benchmark/Mesh_3/concurrency.cpp b/Mesh_3/benchmark/Mesh_3/concurrency.cpp
index 7b97296a216..73d7aa23196 100644
--- a/Mesh_3/benchmark/Mesh_3/concurrency.cpp
+++ b/Mesh_3/benchmark/Mesh_3/concurrency.cpp
@@ -45,6 +45,7 @@ namespace po = boost::program_options;
 // BENCHMARK GENERAL PARAMETERS
 // ==========================================================================
 
+//#define BENCHMARK_WITH_1_TO_MAX_THREADS
 //#define MESH_3_POLYHEDRON_WITH_FEATURES
 //#define MESH_3_IMPLICIT_WITH_FEATURES
 //#define MESH_3_BENCHMARK_EXPORT_TO_MAYA
@@ -572,7 +573,10 @@ bool make_mesh_polyhedron(const std::string &input_filename,
 
   // Triangulation
 #ifdef CONCURRENT_MESH_3
-  typedef CGAL::Mesh_triangulation_3<Mesh_domain, CGAL::Parallel_tag>::type Tr;
+  typedef CGAL::Mesh_triangulation_3<
+    Mesh_domain, 
+    CGAL::Kernel_traits<Mesh_domain>::Kernel,
+    CGAL::Parallel_tag>::type Tr;
 #else
   typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
 #endif
@@ -687,7 +691,10 @@ bool make_mesh_3D_images(const std::string &input_filename,
 
   // Triangulation
 #ifdef CONCURRENT_MESH_3
-  typedef CGAL::Mesh_triangulation_3<Mesh_domain, CGAL::Parallel_tag>::type Tr;
+  typedef CGAL::Mesh_triangulation_3<
+    Mesh_domain, 
+    CGAL::Kernel_traits<Mesh_domain>::Kernel,
+    CGAL::Parallel_tag>::type Tr;
 #else
   typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
 #endif
@@ -732,7 +739,7 @@ bool make_mesh_3D_images(const std::string &input_filename,
   double sliverbound = 4;
 #else
   double timelimit = 0;
-  double sliverbound = 7;
+  double sliverbound = 4;
 #endif
 
   C3t3 c3t3 = CGAL::make_mesh_3<C3t3>( domain
@@ -794,9 +801,12 @@ bool make_mesh_implicit(double facet_approx,
 
   // Triangulation
 #ifdef CONCURRENT_MESH_3
-  typedef typename CGAL::Mesh_triangulation_3<Mesh_domain, CGAL::Parallel_tag>::type Tr;
+  typedef CGAL::Mesh_triangulation_3<
+    Mesh_domain, 
+    CGAL::Kernel_traits<Mesh_domain>::Kernel,
+    CGAL::Parallel_tag>::type Tr;
 #else
-  typedef typename CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
+  typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
 #endif
   // C3t3
   typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
@@ -865,7 +875,7 @@ bool make_mesh_implicit(double facet_approx,
   double sliverbound = 4;
 #else
   double timelimit = 0;
-  double sliverbound = 7;
+  double sliverbound = 4;
 #endif
 
   C3t3 c3t3 = CGAL::make_mesh_3<C3t3>( domain
@@ -959,7 +969,11 @@ int main()
   {
     int i = 1;
 #ifdef CONCURRENT_MESH_3
-    for(num_threads = 2 ; num_threads <= 12 ; ++num_threads) // CJTODO for test
+# ifdef BENCHMARK_WITH_1_TO_MAX_THREADS
+    for(num_threads = 1 ; 
+          num_threads <= task_scheduler_init::default_num_threads() ; 
+          ++num_threads)
+# endif
     /*for (Concurrent_mesher_config::get().num_work_items_per_batch = 5 ;
       Concurrent_mesher_config::get().num_work_items_per_batch < 100 ;
       Concurrent_mesher_config::get().num_work_items_per_batch += 5)*/
diff --git a/Mesh_3/demo/Mesh_3/C3t3_type.h b/Mesh_3/demo/Mesh_3/C3t3_type.h
index 53e9a4309af..fed11c5d178 100644
--- a/Mesh_3/demo/Mesh_3/C3t3_type.h
+++ b/Mesh_3/demo/Mesh_3/C3t3_type.h
@@ -81,7 +81,9 @@ typedef CGAL::Mesh_3::Robust_intersection_traits_3<Kernel>              RKernel;
 
 // Triangulation
 #ifdef CONCURRENT_MESH_3
-  typedef CGAL::Mesh_triangulation_3<Polyhedral_mesh_domain, CGAL::Parallel_tag>::type Tr;
+  typedef CGAL::Mesh_triangulation_3<Polyhedral_mesh_domain, 
+                                     CGAL::Kernel_traits<Polyhedral_mesh_domain>::Kernel,
+                                     CGAL::Parallel_tag>::type Tr;
 #else
   typedef CGAL::Mesh_triangulation_3<Polyhedral_mesh_domain>::type Tr;
 #endif
diff --git a/Mesh_3/include/CGAL/Mesh_triangulation_3.h b/Mesh_3/include/CGAL/Mesh_triangulation_3.h
index 33723803e91..5f9e66409bc 100644
--- a/Mesh_3/include/CGAL/Mesh_triangulation_3.h
+++ b/Mesh_3/include/CGAL/Mesh_triangulation_3.h
@@ -60,13 +60,13 @@ namespace CGAL {
   
 // Struct Mesh_triangulation_3
 //
-template<class MD, 
-         class Concurrency_tag = Sequential_tag,
-         class K=typename Kernel_traits<MD>::Kernel>
+template<class MD,
+         class K=typename Kernel_traits<MD>::Kernel,
+         class Concurrency_tag = Sequential_tag>
 struct Mesh_triangulation_3;
 
 // Sequential version (default)
-template<class MD, class Concurrency_tag, class K>
+template<class MD, class K, class Concurrency_tag>
 struct Mesh_triangulation_3
 {
 private:
@@ -100,7 +100,7 @@ public:
 // Parallel version (specialization)
 //
 template<class MD, class K>
-struct Mesh_triangulation_3<MD, Parallel_tag, K>
+struct Mesh_triangulation_3<MD, K, Parallel_tag>
 {
 private:
   typedef typename details::Mesh_geom_traits_generator<K>::type Geom_traits;