diff --git a/Constrained_triangulation_3/examples/Constrained_triangulation_3/ccdt_3_from_soup.cpp b/Constrained_triangulation_3/examples/Constrained_triangulation_3/ccdt_3_from_soup.cpp
index cbe716e5efd..8ba8a825e2d 100644
--- a/Constrained_triangulation_3/examples/Constrained_triangulation_3/ccdt_3_from_soup.cpp
+++ b/Constrained_triangulation_3/examples/Constrained_triangulation_3/ccdt_3_from_soup.cpp
@@ -5,6 +5,7 @@
 #include <CGAL/make_conforming_constrained_Delaunay_triangulation_3.h>
 
 #include <vector>
+#include <algorithm>
 
 using K = CGAL::Exact_predicates_inexact_constructions_kernel;
 
@@ -29,6 +30,18 @@ int main(int argc, char* argv[])
             << "Number of constrained facets in the CDT: "
             << ccdt.number_of_constrained_facets() << '\n';
 
+  // Collect constrained facets per polygon
+  std::vector<std::size_t> constrained_facets(polygons.size());
+  for(auto facet : ccdt.constrained_facets())
+  {
+    int i = ccdt.face_constraint_index(facet);
+    ++constrained_facets[i];
+  }
+  auto it = std::max_element(constrained_facets.begin(), constrained_facets.end());
+
+  std::cout << "The polygon with the most constrained facets has index "
+            << (it - constrained_facets.begin()) << " and " << *it << " facets.\n";
+
   std::ofstream ofs(argc > 2 ? argv[2] : "out.mesh");
   ofs.precision(17);
   CGAL::IO::write_MEDIT(ofs, ccdt);
diff --git a/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_3.h b/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_3.h
index 6f3207a5852..785ea3cd50b 100644
--- a/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_3.h
+++ b/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_3.h
@@ -1034,7 +1034,7 @@ public:
    */
   CDT_3_signed_index face_constraint_index(typename Triangulation::Cell_handle ch, int i) const
   {
-    return ch->face_id[static_cast<unsigned>(i)];
+    return ch->ccdt_3_data().face_constraint_index(i);
   }
 
   /*!
diff --git a/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_cell_base_3.h b/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_cell_base_3.h
index 7371ee1c888..9581696cafe 100644
--- a/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_cell_base_3.h
+++ b/Constrained_triangulation_3/include/CGAL/Conforming_constrained_Delaunay_triangulation_cell_base_3.h
@@ -98,7 +98,7 @@ public:
         CGAL::read(is, i);
       }
       if(!is) return is;
-      c.face_id[li] = i;
+      c->ccdt_3_data().set_face_constraint_index(li, i);
     }
     return is;
   }