diff --git a/Mesh_2/doc/Mesh_2/Mesh_2.txt b/Mesh_2/doc/Mesh_2/Mesh_2.txt
index fde138a77dc..0947508e51a 100644
--- a/Mesh_2/doc/Mesh_2/Mesh_2.txt
+++ b/Mesh_2/doc/Mesh_2/Mesh_2.txt
@@ -264,9 +264,9 @@ The center of mass is computed with respect to a sizing function that was design
 preserve the local density of points in the mesh generated by Delaunay refinement.
 
 
-\section Mesh_2Examples Examples
+\subsection Mesh_2Examples Examples
 
-\subsection Mesh_2ExampleUsingtheGlobalFunction Example Using the Global Function
+\subsubsection Mesh_2ExampleUsingtheGlobalFunction Example Using the Global Function
 
 The following example inserts several segments into a constrained
 triangulation and then meshes it using the global function
@@ -277,7 +277,7 @@ unbounded component.
 
 \cgalExample{Mesh_2/mesh_global.cpp}
 
-\subsection Mesh_2ExampleUsingtheClass Example Using the Class Delaunay_mesher_2<CDT>
+\subsubsection Mesh_2ExampleUsingtheClass Example Using the Class Delaunay_mesher_2<CDT>
 
 This example uses the class `Delaunay_mesher_2<CDT>` and calls
 the `refine_mesh()` member function twice, changing the size and
@@ -288,7 +288,7 @@ built twice.
 
 \cgalExample{Mesh_2/mesh_class.cpp}
 
-\subsection Mesh_2ExampleUsingSeeds Example Using Seeds
+\subsubsection Mesh_2ExampleUsingSeeds Example Using Seeds
 
 This example uses the global function `refine_Delaunay_mesh_2()` but
 defines a domain by using one seed. The size and shape criteria are the
@@ -301,10 +301,10 @@ faces is used to count them.
 \cgalExample{Mesh_2/mesh_with_seeds.cpp}
 
 
-\subsection Mesh_2ExampleLloyd Example Using the Lloyd optimizer
+\subsubsection Mesh_2ExampleLloyd Example Using the Lloyd optimizer
 
 This example uses the global function `lloyd_optimize_mesh_2()`. 
-The mesh is generated using the function `refine_mesh()` of `CGAL::Delaunay_mesher_2`,
+The mesh is generated using the function `refine_Delaunay_mesh_2()` of `CGAL::Delaunay_mesher_2`,
 and is then optimized using `lloyd_optimize_mesh_2()`. The optimization will stop 
 after 10 (set by `max_iteration_number`) iterations of alternating vertex relocations
 and Delaunay connectivity updates. More termination conditions can be used and are detailed