diff --git a/Polygon/include/CGAL/Polygon_with_holes_2.h b/Polygon/include/CGAL/Polygon_with_holes_2.h
index 032b2c52084d..e7178d650cae 100644
--- a/Polygon/include/CGAL/Polygon_with_holes_2.h
+++ b/Polygon/include/CGAL/Polygon_with_holes_2.h
@@ -30,7 +30,7 @@ namespace CGAL {
 The class `Polygon_with_holes_2` models the concept `GeneralPolygonWithHoles_2`.
 It represents a linear polygon with holes. It is parameterized with two
 types (`Kernel` and `Container`) that are used to instantiate
-the type `Polygon_2<Kernel,Container>`. This poygon type is used to
+the type `Polygon_2<Kernel,Container>`. This polygon type is used to
 represent the outer boundary and the boundary of the holes (if any exist).
 
 \cgalModels{GeneralPolygonWithHoles_2}
@@ -42,7 +42,7 @@ class Polygon_with_holes_2 :
   public General_polygon_with_holes_2<CGAL::Polygon_2<Kernel, Containter> >
 {
 public:
-
+  typedef Kernel                                     Traits;
   typedef CGAL::Polygon_2<Kernel, Containter>        Polygon_2;
   typedef General_polygon_with_holes_2<Polygon_2>    Base;
   typedef typename Base::Hole_const_iterator         Hole_const_iterator;
diff --git a/Polygon_repair/examples/Polygon_repair/repair_union_intersect_2.cpp b/Polygon_repair/examples/Polygon_repair/repair_union_intersect_2.cpp
index b8e5a9c752b8..f4d13ddaafb7 100644
--- a/Polygon_repair/examples/Polygon_repair/repair_union_intersect_2.cpp
+++ b/Polygon_repair/examples/Polygon_repair/repair_union_intersect_2.cpp
@@ -14,6 +14,8 @@
 
 using K = CGAL::Exact_predicates_inexact_constructions_kernel;
 
+using Point_2 = K::Point_2;
+using Polygon_2 = CGAL::Polygon_2<K>;
 using Polygon_with_holes_2 = CGAL::Polygon_with_holes_2<K>;
 using Multipolygon_with_holes_2 = CGAL::Multipolygon_with_holes_2<K>;
 
@@ -45,6 +47,14 @@ main(int argc, char* argv[])
     CGAL::draw(mpwh);
   }
 
-
+  {
+    Polygon_2 pB;
+    pB.push_back(Point_2(-1,-1));
+    pB.push_back(Point_2(1,-1));
+    pB.push_back(Point_2(1,1));
+    pB.push_back(Point_2(-1,1));
+    mpwh = CGAL::Polygon_repair::join(pA,pB);
+    CGAL::draw(mpwh);
+  }
   return 0;
 }
diff --git a/Polygon_repair/include/CGAL/Polygon_repair/Boolean.h b/Polygon_repair/include/CGAL/Polygon_repair/Boolean.h
index 35abad35d3ab..b794ecd9489d 100644
--- a/Polygon_repair/include/CGAL/Polygon_repair/Boolean.h
+++ b/Polygon_repair/include/CGAL/Polygon_repair/Boolean.h
@@ -135,6 +135,22 @@ default constructor.
 /*!
 sets the polygons as input of the %Boolean operation.
 */
+  void
+  insert(const Polygon_2& pA)
+  {
+    cdt.insert_constraint(pA.vertices_begin(), pA.vertices_end(), true);
+  }
+
+
+  void
+  insert(const Polygon_with_holes_2& pwh)
+  {
+    cdt.insert_constraint(pwh.outer_boundary().vertices_begin(), pwh.outer_boundary().vertices_end(), true);
+    for(auto const& hole : pwh.holes()){
+      cdt.insert_constraint(hole.vertices_begin(), hole.vertices_end(), true);
+    }
+  }
+
   void
   insert(const Multipolygon_with_holes_2& pA)
   {
@@ -144,10 +160,7 @@ sets the polygons as input of the %Boolean operation.
         cdt.insert_constraint(hole.vertices_begin(), hole.vertices_end(), true);
       }
     }
-
-    mark_domains();
   }
-
 private:
 
   void
@@ -181,7 +194,7 @@ sets the polygons as input of the %Boolean operation.
     }
   }
 
-
+  public:
   // this marks how many multipolygon interiors overlap a cell of the arrangement of mutipolygons
   void
   mark_domains()
@@ -217,7 +230,7 @@ sets the polygons as input of the %Boolean operation.
     }
   }
 
-
+private:
   template <typename Fct>
   void
   label_domain(Face_handle start, int label, const Fct& fct)
@@ -378,26 +391,45 @@ template <typename K>
 Multipolygon_with_holes_2<K>
 join(const Multipolygon_with_holes_2<K>& pA)
 {
-  CGAL::Polygon_repair::Boolean<K> bops;
-  bops.insert(pA);
   struct Larger_than_zero {
     bool operator()(int i) const
     {
       return i > 0;
     }
   };
+
+  CGAL::Polygon_repair::Boolean<K> bops;
+  bops.insert(pA);
+  bops.mark_domains();
   Larger_than_zero ltz;
   return bops(ltz);
 }
 
+template <typename PA, typename PB, typename K = Default>
+decltype(auto) // Multipolygon_with_holes_2<K>
+join(const PA& pA, const PB& pB, const K& k = Default())
+{
+  typedef typename Default::Get<K, typename PA::Traits>::type Traits;
 
+  struct Larger_than_zero {
+    bool operator()(int i) const
+    {
+      return i > 0;
+    }
+  };
+
+  CGAL::Polygon_repair::Boolean<Traits> bops;
+  bops.insert(pA);
+  bops.insert(pB);
+  bops.mark_domains();
+  Larger_than_zero ltz;
+  return bops(ltz);
+}
 
 template <typename K>
 Multipolygon_with_holes_2<K>
 intersection(const Multipolygon_with_holes_2<K>& pA)
 {
-  CGAL::Polygon_repair::Boolean<K> bops;
-  bops.insert(pA);
   struct Equal  {
     int val;
     Equal(int val)
@@ -409,10 +441,35 @@ intersection(const Multipolygon_with_holes_2<K>& pA)
       return i == val;
     }
   };
+
+  CGAL::Polygon_repair::Boolean<K> bops;
+  bops.insert(pA);
+  bops.mark_domains();
   Equal equal(pA.number_of_polygons_with_holes());
   return bops(equal);
 }
 
+template <typename PA, typename PB, typename K = Default>
+decltype(auto)  // Multipolygon_with_holes_2<K>
+intersection(const PA& pA, const PB& pB, const K& k = Default())
+{
+  typedef typename Default::Get<K, typename PA::Traits>::type Traits;
+
+  struct Equal  {
+    bool operator()(int i) const
+    {
+      return i == 2;
+    }
+  };
+
+  CGAL::Polygon_repair::Boolean<Traits> bops;
+  bops.insert(pA);
+  bops.insert(pB);
+  bops.mark_domains();
+  Equal equal;
+  return bops(equal);
+}
+
 } // namespace Polygon_repair
 } //namespace CGAL
 
diff --git a/Polygon_repair/include/CGAL/Polygon_repair/repair.h b/Polygon_repair/include/CGAL/Polygon_repair/repair.h
index 33f88d069380..51c81c3229f3 100644
--- a/Polygon_repair/include/CGAL/Polygon_repair/repair.h
+++ b/Polygon_repair/include/CGAL/Polygon_repair/repair.h
@@ -109,14 +109,16 @@ 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, Union_rule)
 {
-  CGAL::Polygon_repair::Boolean<Kernel> bops;
-  bops.insert(p);
   struct Larger_than_zero {
     bool operator()(int i) const
     {
       return i > 0;
     }
   };
+
+  CGAL::Polygon_repair::Boolean<Kernel> bops;
+  bops.insert(p);
+  bops.mark_domains();
   Larger_than_zero ltz;
   return bops(ltz);
 }
@@ -125,8 +127,6 @@ 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, Intersection_rule)
 {
- CGAL::Polygon_repair::Boolean<Kernel> bops;
-  bops.insert(p);
   struct Equal  {
     int val;
     Equal(int val)
@@ -138,6 +138,10 @@ Multipolygon_with_holes_2<Kernel, Container> repair(const Multipolygon_with_hole
       return i == val;
     }
   };
+
+ CGAL::Polygon_repair::Boolean<Kernel> bops;
+  bops.insert(p);
+  bops.mark_domains();
   Equal equal(p.number_of_polygons_with_holes());
   return bops(equal);
 }