diff --git a/Mesh_2/doc/Mesh_2/CGAL/lloyd_optimize_mesh_2.h b/Mesh_2/doc/Mesh_2/CGAL/lloyd_optimize_mesh_2.h
new file mode 100644
index 00000000000..63b75dad08d
--- /dev/null
+++ b/Mesh_2/doc/Mesh_2/CGAL/lloyd_optimize_mesh_2.h
@@ -0,0 +1,99 @@
+namespace CGAL {
+
+/*!
+\ingroup PkgMesh_2Functions
+
+The function `lloyd_optimize_mesh_2()` is a mesh optimization process 
+based on the minimization of a global energy function. 
+
+In `lloyd_optimize_mesh_2()`, the minimized global energy may be interpreted 
+as the \f$ L^1\f$-norm of the error achieved 
+when the function \f$ x^2\f$ is interpolated on the mesh domain 
+using a piecewise linear function which is linear 
+in each cell of the Voronoi diagram of the mesh vertices. 
+
+The optimizer `lloyd_optimize_mesh_2()` works in iterative steps. 
+At each iteration, mesh vertices are moved into 
+positions that bring to zero the energy gradient 
+and the Delaunay triangulation is updated. 
+Vertices on the mesh boundaries are not moved.
+
+\pre `time_limit` \f$ \geq\f$ 0 and 0 \f$ \leq\f$ `convergence` \f$ \leq\f$ 1 and 0 \f$ \leq\f$ `freeze_bound` \f$ \leq\f$ 1 
+
+\tparam CDT is required to be or derive from 
+`CGAL::Constrained_Delaunay_triangulation_2`.
+The argument `cdt`, passed by reference, provides the initial mesh 
+and is modified by the algorithm to represent the final optimized mesh. 
+
+The function has several optional parameters which are named parameters
+(we use the Boost.Parameter library). 
+Therefore, when calling the function, the parameters can be provided in any order 
+provided that the names of the parameters are used 
+(see example at the bottom of this page). 
+
+\cgalHeading{Named Parameters}
+
+- <b>`parameters::time_limit`</b>
+is used to set up, in seconds, 
+a CPU time limit after which the optimization process is stopped. This time is 
+measured using `Timer`. 
+The default value is 0 and means that there is no time limit. 
+
+- <b>`parameters::%max_iteration_number`</b> sets a limit on the 
+number of performed iterations. The default value of 0 means that there is 
+no limit on the number of performed iterations. 
+
+- <b>`parameters::%convergence`</b> is a stopping criterion based on convergence: 
+the optimization process is stopped, when at the last iteration, 
+the displacement of any vertex is less than a given fraction of the 
+length of the shortest edge incident to that vertex. 
+The parameter `convergence` gives the threshold ratio. 
+
+- <b>`parameters::freeze_bound`</b> is designed to reduce running time of each 
+optimization iteration. Any vertex that has a displacement less than a given
+fraction of the length of its shortest incident edge, is frozen (i.e.\ is 
+not relocated). The parameter `freeze_bound` gives the threshold ratio.
+The default value is 0.001. If it is set to 0, freezing of vertices is disabled.
+
+
+\return
+The function `lloyd_optimize_mesh_2()` returns a value of type `CGAL::Mesh_optimization_return_code` 
+which is:
+<UL> 
+<LI>`CGAL::TIME_LIMIT_REACHED` when the time limit is reached. 
+<LI>`CGAL::MAX_ITERATION_NUMBER_REACHED` when `lloyd_optimize_mesh_2()` stops because it has performed `max_iteration_number` iterations. 
+<LI>`CGAL::CONVERGENCE_REACHED` when `lloyd_optimize_mesh_2()` stops because the convergence criterion 
+is met.
+<LI>`CGAL::ALL_VERTICES_FROZEN` when all vertices have been frozen, when the 
+`freeze_bound` parameter is set to a positive value.
+<LI>`CGAL::CANT_IMPROVE_ANYMORE` when `lloyd_optimize_mesh_2()` stops because 
+most vertices have been frozen, and no better convergence can be reached.
+</UL> 
+
+\cgalHeading{Example}
+
+
+\code{.cpp} 
+// Lloyd-smoothing until convergence reaches 0.01, freezing vertices which 
+// move less than 0.001*shortest_incident_edge_length 
+lloyd_optimize_mesh_2(cdt,
+                      parameters::convergence=0.01, 
+                      parameters::freeze_bound=0.001); 
+
+\endcode
+
+\sa `CGAL::Mesh_optimization_return_code` 
+\sa `CGAL::refine_mesh_2()`
+
+*/
+
+template<typename CDT>
+Mesh_optimization_return_code
+lloyd_optimize_mesh_2(CDT& cdt,
+double parameters::time_limit=0,
+std::size_t parameters::max_iteration_number=0,
+double parameters::convergence=0.02,
+double parameters::freeze_bound = 0.01,
+bool parameters::do_freeze=true);
+
+} /* namespace CGAL */
diff --git a/Mesh_2/examples/Mesh_2/mesh_optimization.cpp b/Mesh_2/examples/Mesh_2/mesh_optimization.cpp
index 7dee4b16979..88d203791e7 100644
--- a/Mesh_2/examples/Mesh_2/mesh_optimization.cpp
+++ b/Mesh_2/examples/Mesh_2/mesh_optimization.cpp
@@ -23,6 +23,8 @@ typedef CGAL::Delaunay_mesher_2<CDT, Criteria>              Mesher;
 typedef CDT::Vertex_handle Vertex_handle;
 typedef CDT::Point Point;
 
+using namespace parameters;
+
 int main()
 {
   CDT cdt;
diff --git a/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h b/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h
index a94838a108c..2b96fe0c832 100644
--- a/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h
+++ b/Mesh_2/include/CGAL/lloyd_optimize_mesh_2.h
@@ -12,6 +12,8 @@
 #include <boost/parameter.hpp>
 #include <boost/parameter/name.hpp>
 
+namespace parameters
+{
 BOOST_PARAMETER_NAME( cdt )
 BOOST_PARAMETER_NAME( (max_iteration_number, tag) max_iteration_number_ )
 BOOST_PARAMETER_NAME( (convergence, tag) convergence_)
@@ -20,6 +22,9 @@ BOOST_PARAMETER_NAME( (freeze_bound, tag) freeze_bound_)
 BOOST_PARAMETER_NAME( (seeds_begin, tag) seeds_begin_)
 BOOST_PARAMETER_NAME( (seeds_end, tag) seeds_end_)
 BOOST_PARAMETER_NAME( (mark, tag) mark_)
+}
+
+using namespace parameters;
 
 namespace CGAL
 {
diff --git a/Mesh_2/test/Mesh_2/test_lloyd.cpp b/Mesh_2/test/Mesh_2/test_lloyd.cpp
index 3a883e59198..9251561b5c1 100644
--- a/Mesh_2/test/Mesh_2/test_lloyd.cpp
+++ b/Mesh_2/test/Mesh_2/test_lloyd.cpp
@@ -16,6 +16,8 @@
 
 typedef CGAL::Exact_predicates_inexact_constructions_kernel Epick;
 
+using namespace parameters;
+
 template <typename K>
 struct Lloyd_tester
 {