diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedIdentifiedVerticalTraits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedIdentifiedVerticalTraits_2.h
deleted file mode 100644
index 3f3e1739a3d..00000000000
--- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedIdentifiedVerticalTraits_2.h
+++ /dev/null
@@ -1,42 +0,0 @@
-/*! \ingroup PkgArrangementOnSurface2ConceptsTraits
- * \cgalConcept
- *
- * `ArrangementClosedIdentifiedVerticalTraits_2` is an abstract concept. It
- * generalizes the concepts `ArrangementClosedLeftTraits_2`,
- * `ArrangementClosedRightTraits_2`, and
- * `ArrangementIdentifiedVerticalTraits_2`. (An "abstract" concept is a concept
- * that is useless on its own.) Only a combination of this concept and one or
- * more concepts that handle curves that either reach or approach the remaining
- * boundary sides (that is, borrom and top) are purposeful, and can have models.
- *
- * \cgalRefines `ArrangementBasicTraits_2`
- *
- * \cgalHasModel `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>`
- *
- * \sa `ArrangementVerticalSideTraits_2`
- */
-class ArrangementVerticalSideTraits_2 {
-public:
-
-  /// \name Categories
-  /// @{
-  /// @}
-
-  /// \name Types
-  /// @{
-  /// @}
-
-  /// \name Functor Types
-  /// @{
-
-  /// models the concept `ArrTraits::CompareYOnBoundary_2`.
-  typedef unspecified_type Compare_y_on_boundary_2;
-
-  /// @}
-
-  /// \name Accessing Functor Objects
-  /// @{
-  Compare_y_on_boundary_2 compare_y_on_boundary_2_object() const;
-  /// @}
-
-}; /* end ArrangementHorizontalSideTraits_2 */
diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedLeftTraits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedLeftTraits_2.h
index 10a03a61880..67722a077a2 100644
--- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedLeftTraits_2.h
+++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedLeftTraits_2.h
@@ -35,7 +35,13 @@ public:
   /// \name Functor Types
   /// @{
 
+  /// models the concept `ArrTraits::CompareYOnBoundary_2`.
+  typedef unspecified_type Compare_y_on_boundary_2;
+
+  /// @}
+
   /// \name Accessing Functor Objects
   /// @{
+  Compare_y_on_boundary_2 compare_y_on_boundary_2_object() const;
   /// @}
-}
+};
diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedRightTraits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedRightTraits_2.h
index a6f0aa75351..15d25b7c742 100644
--- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedRightTraits_2.h
+++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementClosedRightTraits_2.h
@@ -34,7 +34,13 @@ public:
   /// \name Functor Types
   /// @{
 
+  /// models the concept `ArrTraits::CompareYOnBoundary_2`.
+  typedef unspecified_type Compare_y_on_boundary_2;
+
+  /// @}
+
   /// \name Accessing Functor Objects
   /// @{
+  Compare_y_on_boundary_2 compare_y_on_boundary_2_object() const;
   /// @}
-}
+};
diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementIdentifiedVerticalTraits_2.h b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementIdentifiedVerticalTraits_2.h
index ff5d4b8ef31..e5cff1def05 100644
--- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementIdentifiedVerticalTraits_2.h
+++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementIdentifiedVerticalTraits_2.h
@@ -34,6 +34,9 @@ public:
   /// \name Functor Types
   /// @{
 
+  /// models the concept `ArrTraits::CompareYOnBoundary_2`.
+  typedef unspecified_type Compare_y_on_boundary_2;
+
   /// models the concept `ArrTraits::IsOnYIdentification_2`.
   typedef unspecified_type Is_on_y_identification_2;
 
@@ -41,6 +44,7 @@ public:
 
   /// \name Accessing Functor Objects
   /// @{
+  Compare_y_on_boundary_2 compare_y_on_boundary_2_object() const;
   Is_on_y_identification_2 is_on_y_identification_2_object() const;
   /// @}
 }
diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt
index 6bbc3363430..cc7c14bd4b5 100644
--- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt
+++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt
@@ -122,7 +122,6 @@ implemented as peripheral classes or as free (global) functions.
 - `ArrangementTraits_2`
 - `ArrangementHorizontalSideTraits_2`
 - `ArrangementVerticalSideTraits_2`
-- `ArrangementClosedIdentifiedVerticalTraits_2`
 - `ArrangementIdentifiedVerticalTraits_2`
 - `ArrangementIdentifiedHorizontalTraits_2`
 - `ArrangementOpenBoundaryTraits_2`