diff --git a/Mesh_3/demo/Mesh_3/Mesh_3_optimization_plugin_cgal_code.cpp b/Mesh_3/demo/Mesh_3/Mesh_3_optimization_plugin_cgal_code.cpp
index 16260496cbd..8307be69868 100644
--- a/Mesh_3/demo/Mesh_3/Mesh_3_optimization_plugin_cgal_code.cpp
+++ b/Mesh_3/demo/Mesh_3/Mesh_3_optimization_plugin_cgal_code.cpp
@@ -677,8 +677,7 @@ class Optimization_function < Domain, Exude_parameters >
   typedef C3t3::Triangulation                               Tr;
   typedef CGAL::Mesh_3::Min_dihedral_angle_criterion<Tr>    Sc;
   typedef Exude_visitor                                     Visitor;
-  typedef CGAL::Mesh_3::Slivers_exuder<
-                                C3t3,Domain,Sc,Visitor>     Exuder;
+  typedef CGAL::Mesh_3::Slivers_exuder<C3t3,Sc,Visitor>     Exuder;
   
   typedef Optimization_function_base< Domain > Base;
   
@@ -716,7 +715,7 @@ protected:
     if ( NULL != exude_ ) { return CGAL::MESH_OPTIMIZATION_UNKNOWN_ERROR; }
     
     // Create exuder
-    exude_ = new Exuder(c3t3, domain, criterion_);
+    exude_ = new Exuder(c3t3, criterion_);
     if ( NULL == exude_ ) { return CGAL::MESH_OPTIMIZATION_UNKNOWN_ERROR; }
     
     // Set time_limit
diff --git a/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp b/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp
index 66de13b3476..dbc162aa2c4 100644
--- a/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_implicit_ellipsoid.cpp
@@ -60,7 +60,7 @@ int main()
   CGAL::perturb_mesh_3(c3t3, domain, time_limit=5, sliver_bound=12);
   
   // Exudation
-  CGAL::exude_mesh_3(c3t3, domain);
+  CGAL::exude_mesh_3(c3t3);
   
   // Output
   medit_file.open("out_optimized.mesh");
diff --git a/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp b/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp
index 04a2b869653..01b093b893b 100644
--- a/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_optimization_lloyd_example.cpp
@@ -52,7 +52,7 @@ int main()
                                           no_perturb(), no_exude());
   
   CGAL::lloyd_optimize_mesh_3(c3t3_bis, domain, time_limit=30);
-  CGAL::exude_mesh_3(c3t3_bis, domain, sliver_bound=10, time_limit=10);
+  CGAL::exude_mesh_3(c3t3_bis, sliver_bound=10, time_limit=10);
   
   // Output
   std::ofstream medit_file("out.mesh");
diff --git a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
index e27bc1b4c55..426617802c3 100644
--- a/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
+++ b/Mesh_3/include/CGAL/Mesh_3/C3T3_helpers.h
@@ -3393,54 +3393,54 @@ bool
 C3T3_helpers<C3T3,MD>::
 try_lock_and_get_incident_cells(const Vertex_handle& v,
                                 Cell_vector &cells) const
-{
-  // We need to lock v individually first, to be sure v->cell() is valid
-  if (!try_lock_vertex(v))
-    return false;
-
-  Cell_handle d = v->cell();
-  if (!try_lock_element(d)) // LOCK
   {
-    unlock_all_elements();
-    return false;
-  }
-  cells.push_back(d);
-  d->tds_data().mark_in_conflict();
-  int head=0;
-  int tail=1;
-  do {
-    Cell_handle c = cells[head];
+    // We need to lock v individually first, to be sure v->cell() is valid
+    if (!try_lock_vertex(v))
+      return false;
 
-    for (int i=0; i<4; ++i) {
-      if (c->vertex(i) == v)
-        continue;
-      Cell_handle next = c->neighbor(i);
-
-      if (!try_lock_element(next)) // LOCK
-      {
-        BOOST_FOREACH(Cell_handle& ch,
-          std::make_pair(cells.begin(), cells.end()))
-        {
-          ch->tds_data().clear();
-        }
-        cells.clear();
-        unlock_all_elements();
-        return false;
-      }
-      if (! next->tds_data().is_clear())
-        continue;
-      cells.push_back(next);
-      ++tail;
-      next->tds_data().mark_in_conflict();
+    Cell_handle d = v->cell();
+    if (!try_lock_element(d)) // LOCK
+    {
+      unlock_all_elements();
+      return false;
     }
-    ++head;
-  } while(head != tail);
-  BOOST_FOREACH(Cell_handle& ch, std::make_pair(cells.begin(), cells.end()))
-  {
-    ch->tds_data().clear();
+    cells.push_back(d);
+    d->tds_data().mark_in_conflict();
+    int head=0;
+    int tail=1;
+    do {
+      Cell_handle c = cells[head];
+
+      for (int i=0; i<4; ++i) {
+        if (c->vertex(i) == v)
+          continue;
+        Cell_handle next = c->neighbor(i);
+
+        if (!try_lock_element(next)) // LOCK
+        {
+          BOOST_FOREACH(Cell_handle& ch,
+            std::make_pair(cells.begin(), cells.end()))
+          {
+            ch->tds_data().clear();
+          }
+          cells.clear();
+          unlock_all_elements();
+          return false;
+        }
+        if (! next->tds_data().is_clear())
+          continue;
+        cells.push_back(next);
+        ++tail;
+        next->tds_data().mark_in_conflict();
+      }
+      ++head;
+    } while(head != tail);
+    BOOST_FOREACH(Cell_handle& ch, std::make_pair(cells.begin(), cells.end()))
+    {
+      ch->tds_data().clear();
+    }
+    return true;
   }
-  return true;
-}
 
 template <typename C3T3, typename MD>
 template <typename Filter>
diff --git a/Mesh_3/include/CGAL/Mesh_3/Slivers_exuder.h b/Mesh_3/include/CGAL/Mesh_3/Slivers_exuder.h
index 346567ccf8f..14c461fb7b5 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Slivers_exuder.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Slivers_exuder.h
@@ -27,7 +27,6 @@
 
 #include <CGAL/Double_map.h>
 #include <CGAL/iterator.h>
-#include <CGAL/Mesh_3/C3T3_helpers.h>
 #include <map>
 #include <vector>
 #include <set>
@@ -361,7 +360,6 @@ private:
 
 template <
   typename C3T3,
-  typename MeshDomain,
   typename SliverCriteria,
   typename Visitor_ = Null_exuder_visitor<C3T3>,
   typename FT = typename C3T3::Triangulation::Geom_traits::FT
@@ -379,7 +377,7 @@ public: // Types
 
 private: // Types
 
-  typedef Slivers_exuder<C3T3, MeshDomain, SliverCriteria, Visitor_, FT> Self;
+  typedef Slivers_exuder<C3T3, SliverCriteria, Visitor_, FT> Self;
 
   typedef typename C3T3::Triangulation Tr;
   typedef typename Tr::Weighted_point Weighted_point;
@@ -426,10 +424,7 @@ private: // Types
   // Should define
   //  - after_cell_pumped(std::size_t cells_left_number)
   typedef Visitor_ Visitor;
-
-  // Helper
-  typedef class C3T3_helpers<C3T3,MeshDomain> C3T3_helpers;
-
+  
   using Base::get_lock_data_structure;
 
 public: // methods
@@ -442,7 +437,6 @@ public: // methods
    * max_weight(v) < d*dist(v,nearest_vertice(v))
    */
   Slivers_exuder(C3T3& c3t3,
-                 const MeshDomain& domain,
                  const SliverCriteria& criterion,
                  double d = 0.45);
 
@@ -458,9 +452,6 @@ public: // methods
   WallClockTimer t;
 #endif
 
-    // Reset sliver value cache
-    helper_.reset_cache();
-
     Mesh_optimization_return_code ret =
       pump_vertices<true>(sliver_criteria_.sliver_bound(), visitor);
 
@@ -866,7 +857,6 @@ private:
 
   bool initialized_;
   SliverCriteria sliver_criteria_;
-  C3T3_helpers helper_;
 
   // Timer
   double time_limit_;
@@ -931,9 +921,9 @@ private:
 
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
-Slivers_exuder(C3T3& c3t3, const Md& domain, const SC& criteria, double d)
+template <typename C3T3, typename SC, typename V_, typename FT>
+Slivers_exuder<C3T3,SC,V_,FT>::
+Slivers_exuder(C3T3& c3t3, const SC& criteria, double d)
   : Base(c3t3.bbox(),
          Concurrent_mesher_config::get().locking_grid_num_cells_per_axis)
   , c3t3_(c3t3)
@@ -944,7 +934,6 @@ Slivers_exuder(C3T3& c3t3, const Md& domain, const SC& criteria, double d)
   , num_of_treated_vertices_(0)
   , initialized_(false)
   , sliver_criteria_(criteria)
-  , helper_(c3t3_,domain,get_lock_data_structure())
   , time_limit_(-1)
   , running_time_()
 {
@@ -953,10 +942,10 @@ Slivers_exuder(C3T3& c3t3, const Md& domain, const SC& criteria, double d)
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 template <bool pump_vertices_on_surfaces>
 Mesh_optimization_return_code
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 pump_vertices(double sliver_criterion_limit,
               Visitor& visitor)
 {
@@ -1103,10 +1092,10 @@ pump_vertices(double sliver_criterion_limit,
 } // end function pump_vertices
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 template <bool pump_vertices_on_surfaces>
 bool
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 pump_vertex(const Vertex_handle& pumped_vertex,
             bool *could_lock_zone)
 {
@@ -1130,9 +1119,9 @@ pump_vertex(const Vertex_handle& pumped_vertex,
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 void
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 initialize_prestar_and_criterion_values(const Vertex_handle& v,
                                         Pre_star& pre_star,
                                         Sliver_values& criterion_values,
@@ -1143,8 +1132,9 @@ initialize_prestar_and_criterion_values(const Vertex_handle& v,
   // Parallel
   if (could_lock_zone)
   {
-    if (!helper_.try_lock_and_get_incident_cells(v, incident_cells))
+    if (!tr_.try_lock_and_get_incident_cells(v, incident_cells))
     {
+      this->unlock_all_elements();
       *could_lock_zone = false;
       return;
     }
@@ -1183,9 +1173,9 @@ initialize_prestar_and_criterion_values(const Vertex_handle& v,
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 bool
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 expand_prestar(const Cell_handle& cell_to_add,
                const Vertex_handle& pumped_vertex,
                Pre_star& pre_star,
@@ -1279,9 +1269,9 @@ expand_prestar(const Cell_handle& cell_to_add,
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 double
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 get_best_weight(const Vertex_handle& v, bool *could_lock_zone) const
 {
   // Get pre_star and criterion_values
@@ -1364,9 +1354,9 @@ get_best_weight(const Vertex_handle& v, bool *could_lock_zone) const
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
-typename Slivers_exuder<C3T3,Md,SC,V_,FT>::Umbrella
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+template <typename C3T3, typename SC, typename V_, typename FT>
+typename Slivers_exuder<C3T3,SC,V_,FT>::Umbrella
+Slivers_exuder<C3T3,SC,V_,FT>::
 get_umbrella(const Facet_vector& facets,
              const Vertex_handle& v) const
 {
@@ -1387,10 +1377,10 @@ get_umbrella(const Facet_vector& facets,
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 template <bool pump_vertices_on_surfaces>
 void
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 restore_cells_and_boundary_facets(
   const Boundary_facets_from_outside& boundary_facets_from_outside,
   const Vertex_handle& new_vertex)
@@ -1442,9 +1432,9 @@ restore_cells_and_boundary_facets(
 
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
-typename Slivers_exuder<C3T3,Md,SC,V_,FT>::Ordered_edge
-Slivers_exuder<C3T3,Md,SC,V_,FT>::get_opposite_ordered_edge(
+template <typename C3T3, typename SC, typename V_, typename FT>
+typename Slivers_exuder<C3T3,SC,V_,FT>::Ordered_edge
+Slivers_exuder<C3T3,SC,V_,FT>::get_opposite_ordered_edge(
   const Facet& facet,
   const Vertex_handle& vertex) const
 {
@@ -1472,9 +1462,9 @@ Slivers_exuder<C3T3,Md,SC,V_,FT>::get_opposite_ordered_edge(
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 void
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 restore_internal_facets(const Umbrella& umbrella,
                         const Vertex_handle& new_vertex)
 {
@@ -1500,10 +1490,10 @@ restore_internal_facets(const Umbrella& umbrella,
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 template <bool pump_vertices_on_surfaces>
 void
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 update_mesh(const Weighted_point& new_point,
             const Vertex_handle& old_vertex,
             bool *could_lock_zone)
@@ -1565,10 +1555,10 @@ update_mesh(const Weighted_point& new_point,
 
 #ifdef CGAL_LINKED_WITH_TBB
 // For parallel version
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 template <bool pump_vertices_on_surfaces>
 void
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 enqueue_task(Cell_handle ch, unsigned int erase_counter, double value)
 {
   this->enqueue_work(
@@ -1580,10 +1570,10 @@ enqueue_task(Cell_handle ch, unsigned int erase_counter, double value)
 
 
 #ifdef CGAL_MESH_3_DEBUG_SLIVERS_EXUDER
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 template <class Input_facet_it>
 bool
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 check_pre_star(const Pre_star& pre_star,
                Input_facet_it begin,
                Input_facet_it end,
@@ -1687,9 +1677,9 @@ check_pre_star(const Pre_star& pre_star,
 
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 bool
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 check_pre_star(const Pre_star& pre_star,
                const Weighted_point& wp,
                const Vertex_handle& vh) const
@@ -1716,9 +1706,9 @@ check_pre_star(const Pre_star& pre_star,
 }
 
 
-template <typename C3T3, typename Md, typename SC, typename V_, typename FT>
+template <typename C3T3, typename SC, typename V_, typename FT>
 bool
-Slivers_exuder<C3T3,Md,SC,V_,FT>::
+Slivers_exuder<C3T3,SC,V_,FT>::
 check_ratios(const Sliver_values& criterion_values,
                   const Weighted_point& wp,
                   const Vertex_handle& vh) const
diff --git a/Mesh_3/include/CGAL/exude_mesh_3.h b/Mesh_3/include/CGAL/exude_mesh_3.h
index ce24b1dfa20..de3eecf9986 100644
--- a/Mesh_3/include/CGAL/exude_mesh_3.h
+++ b/Mesh_3/include/CGAL/exude_mesh_3.h
@@ -38,34 +38,32 @@ BOOST_PARAMETER_FUNCTION(
   (Mesh_optimization_return_code),
   exude_mesh_3,
   parameters::tag,
-  (required (in_out(c3t3),*) (domain,*) )
+  (required (in_out(c3t3),*) )
   (optional
     (time_limit_, *, 0 )
     (sliver_bound_, *, parameters::default_values::exude_sliver_bound )
   )
 )
 {
-  return exude_mesh_3_impl(c3t3, domain, time_limit_, sliver_bound_);
+  return exude_mesh_3_impl(c3t3, time_limit_, sliver_bound_);
 }
 
 
 
-template <typename C3T3, typename MeshDomain>
+template <typename C3T3>
 Mesh_optimization_return_code
 exude_mesh_3_impl(C3T3& c3t3,
-                  const MeshDomain& domain,
                   const double time_limit,
                   const double sliver_bound)
 {
-  typedef MeshDomain Md;
   typedef typename C3T3::Triangulation Tr;
   typedef Mesh_3::Min_dihedral_angle_criterion<Tr> Sc;
   //typedef Mesh_3::Radius_radio_criterion<Tr> Sc;
-  typedef typename Mesh_3::Slivers_exuder<C3T3, Md, Sc> Exuder;
+  typedef typename Mesh_3::Slivers_exuder<C3T3, Sc> Exuder;
   
   // Create exuder
   Sc criterion(sliver_bound, c3t3.triangulation());
-  Exuder exuder(c3t3, domain, criterion);
+  Exuder exuder(c3t3, criterion);
 
   // Set time_limit
   exuder.set_time_limit(time_limit);
diff --git a/Mesh_3/include/CGAL/refine_mesh_3.h b/Mesh_3/include/CGAL/refine_mesh_3.h
index d7208c8ce06..0c4cc81a56f 100644
--- a/Mesh_3/include/CGAL/refine_mesh_3.h
+++ b/Mesh_3/include/CGAL/refine_mesh_3.h
@@ -463,7 +463,6 @@ void refine_mesh_3_impl(C3T3& c3t3,
       exude_time_limit = exude.time_limit();
     
     exude_mesh_3(c3t3,
-                 domain,
                  parameters::time_limit = exude_time_limit,
                  parameters::sliver_bound = exude.bound());
   }
diff --git a/Mesh_3/test/Mesh_3/test_meshing_utilities.h b/Mesh_3/test/Mesh_3/test_meshing_utilities.h
index 1e81bb73d95..49ee9ed8b52 100644
--- a/Mesh_3/test/Mesh_3/test_meshing_utilities.h
+++ b/Mesh_3/test/Mesh_3/test_meshing_utilities.h
@@ -129,7 +129,7 @@ struct Tester
     // Quality should increase
     C3t3 exude_c3t3(c3t3);
     std::cerr << "Exude...\n";
-    CGAL::exude_mesh_3(exude_c3t3, domain);
+    CGAL::exude_mesh_3(exude_c3t3);
     verify_c3t3(exude_c3t3,domain,domain_type,v,v,f,f);
     verify_c3t3_quality(c3t3,exude_c3t3);
     verify_c3t3_volume(exude_c3t3, volume*0.95, volume*1.05);