diff --git a/Polygon_repair/include/CGAL/Polygon_repair/Winding.h b/Polygon_repair/include/CGAL/Polygon_repair/Winding.h
index c40865c67e7..afb2ee2ea05 100644
--- a/Polygon_repair/include/CGAL/Polygon_repair/Winding.h
+++ b/Polygon_repair/include/CGAL/Polygon_repair/Winding.h
@@ -135,7 +135,7 @@ sets the polygon as input of the winding number computation.
   void
   insert(const Polygon_2& p)
   {
-      Constraint_id cidA = cdt.insert_constraint(p.vertices_begin(), p.vertices_end(), true);
+      cdt.insert_constraint(p.vertices_begin(), p.vertices_end(), true);
   }
 
 /*!
@@ -144,9 +144,9 @@ sets the polygon as input of the winding number computation.
   void
   insert(const Polygon_with_holes_2& pwh)
   {
-      Constraint_id cidA = cdt.insert_constraint(pwh.outer_boundary().vertices_begin(), pwh.outer_boundary().vertices_end(), true);
+      cdt.insert_constraint(pwh.outer_boundary().vertices_begin(), pwh.outer_boundary().vertices_end(), true);
       for(auto const& hole : pwh.holes()){
-        cidA = cdt.insert_constraint(hole.vertices_begin(), hole.vertices_end(), true);
+        cdt.insert_constraint(hole.vertices_begin(), hole.vertices_end(), true);
       }
   }
 
@@ -157,9 +157,9 @@ sets the polygon as input of the winding number computation.
   insert(const Multipolygon_with_holes_2& mpwh)
   {
     for(const auto& pwh : mpwh.polygons_with_holes()){
-      Constraint_id cidA = cdt.insert_constraint(pwh.outer_boundary().vertices_begin(), pwh.outer_boundary().vertices_end(), true);
+      cdt.insert_constraint(pwh.outer_boundary().vertices_begin(), pwh.outer_boundary().vertices_end(), true);
       for(auto const& hole : pwh.holes()){
-        cidA = cdt.insert_constraint(hole.vertices_begin(), hole.vertices_end(), true);
+        cdt.insert_constraint(hole.vertices_begin(), hole.vertices_end(), true);
       }
     }
   }
diff --git a/Polygon_repair/include/CGAL/Polygon_repair/repair.h b/Polygon_repair/include/CGAL/Polygon_repair/repair.h
index 03961636059..d60519226b8 100644
--- a/Polygon_repair/include/CGAL/Polygon_repair/repair.h
+++ b/Polygon_repair/include/CGAL/Polygon_repair/repair.h
@@ -77,6 +77,17 @@ Multipolygon_with_holes_2<Kernel, Container> repair(const Polygon_with_holes_2<K
 }
 
 
+template <class Kernel, class Container>
+Multipolygon_with_holes_2<Kernel, Container> repair(const Polygon_2<Kernel, Container>& p, Non_zero_rule)
+{
+  Winding<Kernel> winding;
+  winding.insert(p);
+  winding.label();
+  winding.label_domains();
+  return winding();
+}
+
+
 template <class Kernel, class Container>
 Multipolygon_with_holes_2<Kernel, Container> repair(const Polygon_with_holes_2<Kernel, Container>& p, Non_zero_rule)
 {
@@ -93,7 +104,8 @@ Multipolygon_with_holes_2<Kernel, Container> repair(const Polygon_with_holes_2<K
 /// \tparam Kernel parameter of the input and output polygons. Must be model of `ConstrainedDelaunayTriangulationTraits_2 `
 /// \tparam Container parameter of the input and output polygons
 /// \tparam Rule may be any \ref PkgPolygonRepairRules
-/// \pre If the rule is the `Union_rule` or `Non_zero_rule`, each polygon with hole must be free of self-intersections
+/// \pre If the rule is the `Union_rule` or `Non_zero_rule`, each polygon with hole must be free of self-intersections,
+///      the outer boundary of each polygon with holes must be counterclockwise  and the  holes clockwise oriented.
 template <class Kernel, class Container, class Rule = Even_odd_rule>
 Multipolygon_with_holes_2<Kernel, Container> repair(const Multipolygon_with_holes_2<Kernel, Container>& p, Rule = Rule())
 {
@@ -107,6 +119,17 @@ Multipolygon_with_holes_2<Kernel, Container> repair(const Multipolygon_with_hole
 }
 
 
+template <class Kernel, class Container>
+Multipolygon_with_holes_2<Kernel, Container> repair(const Multipolygon_with_holes_2<Kernel, Container>& p, Non_zero_rule)
+{
+  Winding<Kernel> winding;
+  winding.insert(p);
+  winding.label();
+  winding.label_domains();
+  return winding();
+}
+
+
 template <class Kernel, class Container>
 Multipolygon_with_holes_2<Kernel, Container> repair(const Multipolygon_with_holes_2<Kernel, Container>& p, Union_rule)
 {
@@ -791,7 +814,8 @@ protected:
 /// computes the union of all polygons with holes in `p`
 /// \tparam Kernel parameter of the input and output polygons. Must be model of `ConstrainedDelaunayTriangulationTraits_2 `
 /// \tparam Container parameter of the input and output polygons
-/// \pre Each polygon with hole must be free of self-intersections
+/// \pre Each polygon with holes must be free of self-intersections,
+///      the outer boundaries must be counterclockwise and the holes clockwise oriented.
 template <typename Kernel, typename Container>
 Multipolygon_with_holes_2<Kernel,Container>
 join(const Multipolygon_with_holes_2<Kernel,Container>& pa)
@@ -816,7 +840,8 @@ join(const Multipolygon_with_holes_2<Kernel,Container>& pa)
 /// \tparam Container parameter of the input and output polygons
 /// \tparam PA must be `Polygon_2<Kernel, Container>`, or `Polygon_with_holes_2<Kernel, Container>`, or `Multipolygon_with_holes_2<Kernel, Container>`
 /// \tparam PB must be `Polygon_2<Kernel, Container>`, or `Polygon_with_holes_2<Kernel, Container>`, or `Multipolygon_with_holes_2<Kernel, Container>`
-/// \pre The polygons `pa` and `pb` must be free of self-intersections
+/// \pre The polygons `pa` and `pb` must be free of self-intersections,
+///      the outer boundaries must be counterclockwise  and the holes clockwise oriented.
 template <typename PA, typename PB, typename Kernel = Default, typename Container = Default>
 #ifdef DOXYGEN_RUNNING
 Multipolygon_with_holes_2<Kernel,Container>
@@ -848,7 +873,8 @@ join(const PA& pa, const PB& pb, const Kernel& = Default(), const Container& = D
 /// computes the intersection of all polygons with holes in `p`
 /// \tparam Kernel parameter of the input and output polygons. Must be model of `ConstrainedDelaunayTriangulationTraits_2 `
 /// \tparam Container parameter of the input and output polygons
-/// \pre Each polygon with hole must be free of self-intersections
+/// \pre Each polygon with holes must be free of self-intersections
+///      the outer boundaries must be counterclockwise and the holes clockwise oriented.
 template <typename Kernel, typename Container>
 Multipolygon_with_holes_2<Kernel,Container>
 intersect(const Multipolygon_with_holes_2<Kernel,Container>& p)
@@ -880,6 +906,7 @@ intersect(const Multipolygon_with_holes_2<Kernel,Container>& p)
 /// \tparam PA must be `Polygon_2<Kernel, Container>`, or `Polygon_with_holes_2<Kernel, Container>`, or `Multipolygon_with_holes_2<Kernel, Container>`
 /// \tparam PB must be `Polygon_2<Kernel, Container>`, or `Polygon_with_holes_2<Kernel, Container>`, or `Multipolygon_with_holes_2<Kernel, Container>`
 /// \pre The polygons `pa` and `pb` must be free of self-intersections
+///      the outer boundaries must be counterclockwise and the holes clockwise oriented.
 template <typename PA, typename PB, typename Kernel = Default, typename Container = Default>
 #ifdef DOXYGEN_RUNNING
 Multipolygon_with_holes_2<Kernel, Container>
diff --git a/Polygon_repair/test/Polygon_repair/CMakeLists.txt b/Polygon_repair/test/Polygon_repair/CMakeLists.txt
index 1ec7a341fc2..d0424660631 100644
--- a/Polygon_repair/test/Polygon_repair/CMakeLists.txt
+++ b/Polygon_repair/test/Polygon_repair/CMakeLists.txt
@@ -18,6 +18,7 @@ find_package(CGAL REQUIRED OPTIONAL_COMPONENTS Qt6)
 create_single_source_cgal_program( "draw_test_polygons.cpp" )
 create_single_source_cgal_program( "exact_test.cpp")
 create_single_source_cgal_program( "repair_polygon_2_test.cpp" )
+create_single_source_cgal_program( "repair_polygon_non_zero_2_test.cpp" )
 
 if(CGAL_Qt6_FOUND)
   target_link_libraries(draw_test_polygons PRIVATE CGAL::CGAL_Basic_viewer)
diff --git a/Polygon_repair/test/Polygon_repair/repair_polygon_non_zero_2_test.cpp b/Polygon_repair/test/Polygon_repair/repair_polygon_non_zero_2_test.cpp
new file mode 100644
index 00000000000..d289d95e735
--- /dev/null
+++ b/Polygon_repair/test/Polygon_repair/repair_polygon_non_zero_2_test.cpp
@@ -0,0 +1,37 @@
+#include <CGAL/Polygon_repair/repair.h>
+#include <CGAL/IO/WKT.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <iostream>
+#include <fstream>
+#include <sstream>
+#include <string>
+
+using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Point_2 = Kernel::Point_2;
+using Polygon_2 = CGAL::Polygon_2<Kernel>;
+using Polygon_with_holes_2 = CGAL::Polygon_with_holes_2<Kernel>;
+using Multipolygon_with_holes_2 = CGAL::Multipolygon_with_holes_2<Kernel>;
+using Polygon_repair = CGAL::Polygon_repair::Polygon_repair<Kernel>;
+
+int main() {
+
+  std::string polygon("POLYGON((0 0, 3 0, 3 3, 4 3,0 0))");
+  std::istringstream  in(polygon);
+  Polygon_with_holes_2 pwh;
+  CGAL::IO::read_polygon_WKT(in, pwh);
+
+  Polygon_2 outer = pwh.outer_boundary();
+
+  Multipolygon_with_holes_2 rmp;
+
+  rmp = CGAL::Polygon_repair::repair(outer, CGAL::Polygon_repair::Non_zero_rule());
+
+  rmp = CGAL::Polygon_repair::repair(pwh, CGAL::Polygon_repair::Non_zero_rule());
+
+  rmp = CGAL::Polygon_repair::repair(rmp, CGAL::Polygon_repair::Non_zero_rule());
+
+std::cout << "done" << std::endl;
+  return 0;
+}
+