diff --git a/Mesh_3/doc/Mesh_3/CGAL/Mesh_3/parameters.h b/Mesh_3/doc/Mesh_3/CGAL/Mesh_3/parameters.h
index 3a834536db6..018449f3585 100644
--- a/Mesh_3/doc/Mesh_3/CGAL/Mesh_3/parameters.h
+++ b/Mesh_3/doc/Mesh_3/CGAL/Mesh_3/parameters.h
@@ -457,7 +457,7 @@ unspecified_type perturb(const Named_function_parameters& np = parameters::defau
  * The function `parameters::initial_points_generator()` enables the user to specify a functor that follows
  * the `InitialPointsGenerator_3` concept to the mesh generation function `make_mesh_3()`. This functor is called
  * for the initialization of the meshing process, by inserting well-distributed surface vertices.
- * If this parameter is specified without arguments, the default behavior
+ * If this parameter is not specified, the default behavior
  * is executed, which calls the domain's `construct_initial_points_object()` for the initialization of the meshing process.
  *
  * Initialization is considered to be complete if the triangulation is a 3D triangulation
diff --git a/Mesh_3/doc/Mesh_3/Mesh_3.txt b/Mesh_3/doc/Mesh_3/Mesh_3.txt
index 73fc0b179f2..77afe7fd7ea 100644
--- a/Mesh_3/doc/Mesh_3/Mesh_3.txt
+++ b/Mesh_3/doc/Mesh_3/Mesh_3.txt
@@ -757,8 +757,9 @@ First, the functor `construct_intersection` is created:
 then the `%Mesh_domain::Intersection` object (a `%tuple` with three
 elements) is constructed using a call to the functor `construct_intersection`
 \snippet CGAL/Mesh_3/Construct_initial_points_labeled_image.h use construct intersection
-and eventually `%index` is the element \#1 of `%intersect`.
-\snippet CGAL/Mesh_3/Construct_initial_points_labeled_image.h get construct intersection
+and eventually `%intersect_index` is the element \#1 of `%intersect`.
+\snippet CGAL/Mesh_3/Construct_initial_points_labeled_image.h get construct intersection.
+The dimension of the underlying simplex is stored as the element \#2 of `%intersect``.
 
 The result of the custom initialization can be seen in
 \cgalFigureRef{mesh3custominitimage3D}. The generated 3D image contains a