diff --git a/Spatial_sorting/doc/Spatial_sorting/CGAL/hilbert_sort_on_sphere.h b/Spatial_sorting/doc/Spatial_sorting/CGAL/hilbert_sort_on_sphere.h
index 9d21e132c14..bdcb1c47f24 100644
--- a/Spatial_sorting/doc/Spatial_sorting/CGAL/hilbert_sort_on_sphere.h
+++ b/Spatial_sorting/doc/Spatial_sorting/CGAL/hilbert_sort_on_sphere.h
@@ -24,11 +24,7 @@ The input sphere is given by a squared radius and a center, parameter `sqr_radiu
 The default squared radius of the sphere is 1.0.
 The default center of the sphere is the origin (0,0,0).
 
-\cgalHeading{Precondition}
-
-<OL> 
-<LI>`sqr_radius` greater than 0. 
-</OL>
+\pre `sqr_radius` greater than 0.
 
 \cgalHeading{Implementation}
 
diff --git a/Spatial_sorting/doc/Spatial_sorting/CGAL/spatial_sort_on_sphere.h b/Spatial_sorting/doc/Spatial_sorting/CGAL/spatial_sort_on_sphere.h
index 7cf427da1f7..bb673d663cb 100644
--- a/Spatial_sorting/doc/Spatial_sorting/CGAL/spatial_sort_on_sphere.h
+++ b/Spatial_sorting/doc/Spatial_sorting/CGAL/spatial_sort_on_sphere.h
@@ -12,30 +12,23 @@ If input points are not close to the input sphere, this function still works, bu
 
 It sorts the range `[begin, end)` in place. 
 
-The default traits class `Default_traits` is the kernel in which the type 
-`std::iterator_traits<RandomAccessIterator>::%value_type` is defined. 
-
-The default policy is `Hilbert_sort_median_policy()` and the 
-other option is `Hilbert_sort_middle_policy()`. 
-
 The input sphere is given by a squared radius and a center, parameter `sqr_radius` and parameter `center` respectively.
 The default squared radius of the sphere is 1.0.
 The default center of the sphere is the origin (0,0,0).
 
-\cgalHeading{Requirements}
+\tparam InputPointIterator must be a model of `RandomAccessIterator` and
+`std::iterator_traits<InputPointIterator>::%value_type` must be convertible to
+`Traits::Point_3`.
 
-<OL> 
-<LI>`std::iterator_traits<RandomAccessIterator>::%value_type` is convertible to 
-`Traits::Point_3`. 
-<LI>`Traits` is a model for concept `SpatialSortingTraits_3`. 
-</OL> 
+\tparam Traits must be a model for concept `SpatialSortingTraits_3`.
+The default traits class `Default_traits` is the kernel in which the type
+`std::iterator_traits<InputPointIterator>::%value_type` is defined.
 
-\cgalHeading{Precondition}
-
-<OL> 
-<LI>`sqr_radius` greater than 0. 
-</OL>
+\tparam PolicyTag is used to specify the strategy policy.
+Possible values are \link CGAL::Hilbert_sort_median_policy `Hilbert_sort_median_policy` \endlink
+(the default policy) or \link CGAL::Hilbert_sort_middle_policy `Hilbert_sort_middle_policy` \endlink.
 
+\pre `sqr_radius` greater than 0.
 
 \cgalHeading{Implementation}