diff --git a/Installation/CHANGES.md b/Installation/CHANGES.md
index be4ec7fd2b9..208450afaf5 100644
--- a/Installation/CHANGES.md
+++ b/Installation/CHANGES.md
@@ -76,6 +76,9 @@ Release date: October 2023
 -   Added three functions `vertices()` to the class `Triangulation_3`.
     Each of them returns an array containing the vertices of the given triangulation simplex.
 
+### [dD Triangulations](https://doc.cgal.org/6.0/Manual/packages.html#PkgTriangulations)
+-   **Breaking change**: `CGAL::TDS_full_cell_mirror_storage_policy` is now unsupported in dimension larger than 127.
+
 [Release 5.6](https://github.com/CGAL/cgal/releases/tag/v5.6)
 -----------
 
diff --git a/Triangulation/doc/Triangulation/CGAL/Triangulation_ds_full_cell.h b/Triangulation/doc/Triangulation/CGAL/Triangulation_ds_full_cell.h
index 148985c11b7..9aab53b759f 100644
--- a/Triangulation/doc/Triangulation/CGAL/Triangulation_ds_full_cell.h
+++ b/Triangulation/doc/Triangulation/CGAL/Triangulation_ds_full_cell.h
@@ -37,7 +37,7 @@ indices are not stored).
 <LI>`CGAL::TDS_full_cell_default_storage_policy`. In that case, the mirror
 indices are not stored.
 <LI>`CGAL::TDS_full_cell_mirror_storage_policy`. In that case, the mirror
-indices are stored.
+indices are stored. This last policy is not supported when the dimension is larger than 127.
 </UL>
 See the user manual for how to choose the second option.
 
diff --git a/Triangulation/include/CGAL/TDS_full_cell_mirror_storage_policy.h b/Triangulation/include/CGAL/TDS_full_cell_mirror_storage_policy.h
index f3e3bf770d1..63176f5ed30 100644
--- a/Triangulation/include/CGAL/TDS_full_cell_mirror_storage_policy.h
+++ b/Triangulation/include/CGAL/TDS_full_cell_mirror_storage_policy.h
@@ -14,8 +14,8 @@
 
 #include <CGAL/license/Triangulation.h>
 
-
 #include <CGAL/TDS_full_cell_default_storage_policy.h>
+#include <cstdint>
 
 namespace CGAL {
 
@@ -30,7 +30,7 @@ struct   TFC_data< Vertex_handle, Full_cell_handle, Maximal_dimension, TDS_full_
     typedef TFC_data< Vertex_handle, Full_cell_handle, Maximal_dimension, TDS_full_cell_default_storage_policy > Base;
     typedef typename Base::Vertex_handle_array          Vertex_handle_array;
     typedef typename Base::Full_cell_handle_array         Full_cell_handle_array;
-    typedef typename internal::S_or_D_array< int, typename Base::Dimen_plus >   Int_array;
+    typedef typename internal::S_or_D_array< std::int_least8_t, typename Base::Dimen_plus >   Int_array;
 
 private:
     Int_array            mirror_vertices_;
@@ -42,7 +42,7 @@ public:
 
     void set_mirror_index(const int i, const int index)
     {
-        mirror_vertices_[i] = index;
+        mirror_vertices_[i] = static_cast<std::int_least8_t>(index);
     }
     int mirror_index(const int i) const
     {