diff --git a/Mesh_3/examples/Mesh_3/mesh_perturbation_example.cpp b/Mesh_3/examples/Mesh_3/mesh_perturbation_example.cpp
index c6af2736aeb..2a6bcde777a 100644
--- a/Mesh_3/examples/Mesh_3/mesh_perturbation_example.cpp
+++ b/Mesh_3/examples/Mesh_3/mesh_perturbation_example.cpp
@@ -1,3 +1,6 @@
+#define CGAL_MESH_3_VERBOSE
+#define CGAL_MESH_3_PERTURBER_VERBOSE
+
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
 
 #include <CGAL/Mesh_triangulation_3.h>
@@ -45,7 +48,7 @@ int main()
   C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, no_perturb(), no_exude());
 
   // Mesh perturbation
-  CGAL::perturb_mesh_3(c3t3, domain, time_limit=15);
+  CGAL::perturb_mesh_3(c3t3, domain, time_limit=15, sliver_bound=10);
 
   // Output
   std::ofstream medit_file("out.mesh");
diff --git a/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h b/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h
index 88002c5e247..acaf6c08a06 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Sliver_perturber.h
@@ -45,6 +45,7 @@
 #include <CGAL/Mesh_optimization_return_code.h>
 #include <CGAL/Timer.h>
 #include <CGAL/Mesh_3/Null_perturber_visitor.h>
+#include <CGAL/Mesh_3/sliver_criteria.h>
 
 #include <boost/format.hpp>
 #ifdef CGAL_MESH_3_USE_RELAXED_HEAP
@@ -64,7 +65,8 @@ namespace Mesh_3 {
   
 template < typename C3T3,
            typename MeshDomain,
-           typename SliverCriterion,
+           typename SliverCriterion = Mesh_3::Min_dihedral_angle_criterion
+                                  <typename C3T3::Triangulation::Geom_traits>,
            typename Visitor_ = Null_perturber_visitor<C3T3> >
 class Sliver_perturber
 {
@@ -233,8 +235,7 @@ public:
    * The perturber runs step by step, using delta as step size. 
    */
   Mesh_optimization_return_code
-  operator()(const FT& sliver_bound = SliverCriterion::max_value,
-             const FT& delta = FT(1.),
+  operator()(const FT& delta = FT(1.),
              Visitor visitor = Visitor());
   
   /**
@@ -245,6 +246,10 @@ public:
   /// Time accessors
   void set_time_limit(double time) { time_limit_ = time; }
   double time_limit() const { return time_limit_; }
+
+  /// Sliver bound
+  void set_sliver_bound(double bound) { sliver_bound_ = bound; }
+  double sliver_bound() const { return sliver_bound_; }
  
 private:
 
@@ -342,8 +347,8 @@ private:
   Tr& tr_;
   const MeshDomain& domain_;
   double sliver_bound_;
-  Perturbation_vector perturbation_vector_;
   SliverCriterion sliver_criterion_;
+  Perturbation_vector perturbation_vector_;
   C3T3_helpers helper_;
   
   // Internal perturbation ordering
@@ -368,6 +373,7 @@ Sliver_perturber(C3T3& c3t3,
   : c3t3_(c3t3)
   , tr_(c3t3_.triangulation())
   , domain_(domain)
+  , sliver_bound_(Sc::max_value)
   , sliver_criterion_(criterion)
   , helper_(c3t3_,domain_)
   , next_perturbation_order_(0)
@@ -380,7 +386,7 @@ Sliver_perturber(C3T3& c3t3,
 template <typename C3T3, typename Md, typename Sc, typename V_>
 Mesh_optimization_return_code
 Sliver_perturber<C3T3,Md,Sc,V_>::
-operator()(const FT& sliver_bound, const FT& delta, Visitor visitor)
+operator()(const FT& delta, Visitor visitor)
 {
   // Reset sliver value cache
   helper_.reset_cache();
@@ -407,7 +413,7 @@ operator()(const FT& sliver_bound, const FT& delta, Visitor visitor)
   
   FT current_bound = delta;
   bool perturbation_ok = true;
-  while ( current_bound <= sliver_bound && perturbation_ok)
+  while ( current_bound <= sliver_bound() && perturbation_ok)
   {
 #ifdef CGAL_MESH_3_PERTURBER_HIGH_VERBOSITY
     // reset_perturbation_counters is not const
@@ -418,10 +424,10 @@ operator()(const FT& sliver_bound, const FT& delta, Visitor visitor)
     visitor.bound_reached(current_bound);
     
     current_bound += delta;
-    if ( (current_bound >= sliver_bound)
-        && (current_bound < sliver_bound + delta) )
+    if ( (current_bound >= sliver_bound())
+        && (current_bound < sliver_bound() + delta) )
     { 
-      current_bound = sliver_bound;
+      current_bound = sliver_bound();
     }
   }
   
diff --git a/Mesh_3/include/CGAL/Mesh_3/global_parameters.h b/Mesh_3/include/CGAL/Mesh_3/global_parameters.h
index b024ab5d9e6..1652a3ff311 100644
--- a/Mesh_3/include/CGAL/Mesh_3/global_parameters.h
+++ b/Mesh_3/include/CGAL/Mesh_3/global_parameters.h
@@ -61,6 +61,7 @@ BOOST_PARAMETER_NAME( criteria )
   
 BOOST_PARAMETER_NAME( (time_limit, tag) time_limit_ )
 BOOST_PARAMETER_NAME( (sliver_bound, tag) sliver_bound_)
+BOOST_PARAMETER_NAME( (sliver_criterion, tag) sliver_criterion_)
 BOOST_PARAMETER_NAME( (freeze_bound, tag) freeze_bound_)
 BOOST_PARAMETER_NAME( (do_freeze, tag) do_freeze_)
 BOOST_PARAMETER_NAME( (max_iteration_number, tag) max_iteration_number_ )
diff --git a/Mesh_3/include/CGAL/Mesh_3/parameters_defaults.h b/Mesh_3/include/CGAL/Mesh_3/parameters_defaults.h
index c651d1fea44..f63fc6f1808 100644
--- a/Mesh_3/include/CGAL/Mesh_3/parameters_defaults.h
+++ b/Mesh_3/include/CGAL/Mesh_3/parameters_defaults.h
@@ -26,6 +26,8 @@
 #ifndef CGAL_MESH_3_PARAMETERS_DEFAULTS_H
 #define CGAL_MESH_3_PARAMETERS_DEFAULTS_H
 
+#include <CGAL/Mesh_3/sliver_criteria.h>
+
 namespace CGAL {
 namespace parameters { namespace default_values {
 
@@ -34,6 +36,14 @@ const double exude_sliver_bound = 0.;
 
 // perturb_mesh_3
 const double perturb_sliver_bound = 0.;
+template<typename C3T3>
+CGAL::Mesh_3::Min_dihedral_angle_criterion
+  <typename C3T3::Triangulation::Geom_traits> 
+  default_sliver_criterion(const C3T3&)
+{
+  typedef typename C3T3::Triangulation::Geom_traits Gt;
+  return CGAL::Mesh_3::Min_dihedral_angle_criterion<Gt>();
+}
 
 // global optimizers
 const bool do_freeze = true;
diff --git a/Mesh_3/include/CGAL/Mesh_3/sliver_criteria.h b/Mesh_3/include/CGAL/Mesh_3/sliver_criteria.h
index 73101bce55f..1c971190856 100644
--- a/Mesh_3/include/CGAL/Mesh_3/sliver_criteria.h
+++ b/Mesh_3/include/CGAL/Mesh_3/sliver_criteria.h
@@ -32,9 +32,17 @@ namespace CGAL {
 
 namespace Mesh_3 {
 
+template<typename K>
+class Sliver_criterion
+{
+  typedef typename K::Tetrahedron_3 Tetrahedron_3;
+  
+public:
+  virtual double operator()(const Tetrahedron_3& t) const = 0;
+};
   
 template <typename K>
-class Min_dihedral_angle_criterion
+class Min_dihedral_angle_criterion : public Sliver_criterion<K>
 {
   typedef typename K::Tetrahedron_3 Tetrahedron_3;
   
@@ -55,7 +63,7 @@ template<typename K> double Min_dihedral_angle_criterion<K>::max_value = 90.;
 template<typename K> double Min_dihedral_angle_criterion<K>::min_value = 0.; 
   
 template <typename K>
-class Radius_radio_criterion
+class Radius_radio_criterion : public Sliver_criterion<K>
 {
   typedef typename K::Tetrahedron_3 Tetrahedron_3;
   
diff --git a/Mesh_3/include/CGAL/perturb_mesh_3.h b/Mesh_3/include/CGAL/perturb_mesh_3.h
index 5f2b000b9b1..9cf14643fb2 100644
--- a/Mesh_3/include/CGAL/perturb_mesh_3.h
+++ b/Mesh_3/include/CGAL/perturb_mesh_3.h
@@ -42,25 +42,29 @@ BOOST_PARAMETER_FUNCTION(
   (optional
     (time_limit_, *, 0 )
     (sliver_bound_, *, parameters::default_values::perturb_sliver_bound )
+    (sliver_criterion_, *, 
+       parameters::default_values::default_sliver_criterion(c3t3))
   )
 )
 {
-  return perturb_mesh_3_impl(c3t3, domain, time_limit_, sliver_bound_);
+  return perturb_mesh_3_impl(c3t3, domain, time_limit_, sliver_criterion_, sliver_bound_);
 }
 
 
 
-template <typename C3T3, typename MeshDomain> 
+template <typename C3T3, 
+          typename MeshDomain, 
+          typename SliverCriterion> 
 Mesh_optimization_return_code
 perturb_mesh_3_impl(C3T3& c3t3,
                     const MeshDomain& domain,
                     const double time_limit,
+                    const SliverCriterion& sliver_criterion,
                     const double sliver_bound)
 {
   typedef MeshDomain Md;
   typedef typename C3T3::Triangulation::Geom_traits Gt;
-  typedef Mesh_3::Min_dihedral_angle_criterion<Gt> Sc;
-  //typedef Mesh_3::Radius_radio_criterion<Gt> Sc;
+  typedef SliverCriterion Sc;
   
   typedef Mesh_3::Sliver_perturber<C3T3,Md,Sc>            Perturber;
   typedef Mesh_3::Sq_radius_perturbation<C3T3,Md,Sc>      Sq_radius;
@@ -78,12 +82,12 @@ perturb_mesh_3_impl(C3T3& c3t3,
 
   // Set max time
   perturber.set_time_limit(time_limit);
+
+  // Set sliver bound
+  perturber.set_sliver_bound(sliver_bound);
   
   // Launch perturber
-  if ( sliver_bound != 0 )
-    return perturber(sliver_bound);
-  else
-    return perturber();
+  return perturber();
 }