diff --git a/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConformingConstrainedDelaunayTriangulationTraits_3.h b/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConformingConstrainedDelaunayTriangulationTraits_3.h
index 03277d810bb..01fb288edd1 100644
--- a/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConformingConstrainedDelaunayTriangulationTraits_3.h
+++ b/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConformingConstrainedDelaunayTriangulationTraits_3.h
@@ -30,11 +30,6 @@ public:
   */
   using Vector_3 = unspecified_type;
 
-  /*!
-   * A constructor object model of `ConstructVertex_3`
-   */
-  using Construct_vertex_3 = unspecified_type;
-
   /// @}
 
   /// \name Operations
@@ -94,7 +89,7 @@ public:
   /*!
    * returns a function object model of `ConstructVertex_3`
    */
-  Construct_vertex_3 construct_vertex_3_object();
+  unspecified_type construct_vertex_3_object();
 
   /*!
    * returns a predicate object model of `IsDegenerate_3`
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 a4ac3710537..d112bc9065f 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
@@ -131,8 +131,8 @@ does_first_triangle_intersect_second_triangle_interior(const typename K::Triangl
   CGAL_kernel_precondition(!k.is_degenerate_3_object() (t1) );
   CGAL_kernel_precondition(!k.is_degenerate_3_object() (t2) );
 
-  typename K::Construct_vertex_3 vertex_on = k.construct_vertex_3_object();
-  typename K::Orientation_3 orientation = k.orientation_3_object();
+  auto vertex_on = k.construct_vertex_3_object();
+  auto orientation = k.orientation_3_object();
 
   const Point_3& p = vertex_on(t1,0);
   const Point_3& q = vertex_on(t1,1);