diff --git a/Mesh_2/examples/Mesh_2/mesh_optimization.cpp b/Mesh_2/examples/Mesh_2/mesh_optimization.cpp
index 3d10e1e113d..1b23c60e7f5 100644
--- a/Mesh_2/examples/Mesh_2/mesh_optimization.cpp
+++ b/Mesh_2/examples/Mesh_2/mesh_optimization.cpp
@@ -49,7 +49,9 @@ int main()
   std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
 
   std::cout << "Run Lloyd optimization...";
-  CGAL::lloyd_optimize_mesh_2(cdt, 10);
+  CGAL::lloyd_optimize_mesh_2(cdt,
+    convergence = 0,
+    time_limit = 10);
   std::cout << " done." << std::endl;
 
   std::cout << "Number of vertices: " << cdt.number_of_vertices() << std::endl;
diff --git a/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h b/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h
index efe9247a3d6..4d4dfaca5a1 100644
--- a/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h
+++ b/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h
@@ -6,19 +6,52 @@
 #include <CGAL/Mesh_2/Mesh_sizing_field.h>
 #include <fstream>
 
+#include <boost/parameter.hpp>
+#include <boost/parameter/name.hpp>
+
+BOOST_PARAMETER_NAME( cdt )
+BOOST_PARAMETER_NAME( (max_iteration_number, tag) max_iteration_number_ )
+BOOST_PARAMETER_NAME( (convergence, tag) convergence_)
+BOOST_PARAMETER_NAME( (time_limit, tag) time_limit_ )
+BOOST_PARAMETER_NAME( (freeze_bound, tag) freeze_bound_)
+
 namespace CGAL
 {
+  BOOST_PARAMETER_FUNCTION(
+  (void),
+  lloyd_optimize_mesh_2,
+  tag,
+  (required (in_out(cdt),*))
+  (optional
+    (max_iteration_number_, *, 0 )
+    (convergence_, *, 0.001 )
+    (time_limit_, *, 0. )
+    (freeze_bound_, *, 0.001 )
+    )
+  )
+  {
+    return lloyd_optimize_mesh_2_impl(cdt,
+      max_iteration_number_,
+      convergence_,
+      freeze_bound_,
+      time_limit_);
+  }
 
   template<typename CDT>
-  void lloyd_optimize_mesh_2(CDT& cdt,
-                             const unsigned int nb_iterations = 1,
-                             const double convergence_ratio = 0.001)
+  void lloyd_optimize_mesh_2_impl(CDT& cdt,
+                             const unsigned int max_iterations,
+                             const double convergence_ratio,
+                             const double freeze_bound,
+                             const double time_limit)
   {
     typedef Mesh_2::Mesh_sizing_field<CDT>           Sizing;
     typedef Mesh_2::Lloyd_move_2<CDT, Sizing>        Mv;
     typedef Mesh_2::Mesh_global_optimizer_2<CDT, Mv> Optimizer;
 
-    Optimizer lloyd(cdt, convergence_ratio);
+    Optimizer lloyd(cdt,
+                    convergence_ratio,
+                    freeze_bound);
+    lloyd.set_time_limit(time_limit);
 
 #ifdef CGAL_MESH_2_OPTIMIZERS_DEBUG
     std::ofstream os("before_lloyd.angles.txt");
@@ -26,6 +59,11 @@ namespace CGAL
     os.close();
 #endif
 
+    // 1000 iteration max to avoid infinite loop
+    int nb_iterations = (0 == max_iterations)
+      ? 1000
+      : max_iterations;
+
     //run optimization
     lloyd(nb_iterations);