diff --git a/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h b/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
index f9290a3d3d2..dcae81a0e7b 100644
--- a/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
+++ b/Intersections_2/include/CGAL/Ray_2_Iso_rectangle_2_intersection.h
@@ -42,14 +42,15 @@ template <class K>
 class Ray_2_Iso_rectangle_2_pair {
 public:
     enum Intersection_results {NO_INTERSECTION, POINT, SEGMENT};
-    Ray_2_Iso_rectangle_2_pair() ;
     Ray_2_Iso_rectangle_2_pair(typename K::Ray_2 const *ray,
-                          typename K::Iso_rectangle_2 const *rect) ;
+                          typename K::Iso_rectangle_2 const *iso)
+      : _known(false), _ref_point(ray->source()), _dir(ray->direction().to_vector()),
+        _isomin((iso->min)()), _isomax((iso->max)()), _min((typename K::FT)(0)) {}
 
-  Intersection_results intersection_type() const;
+    Intersection_results intersection_type() const;
 
-    bool intersection( typename K::Point_2 &result) const;
-    bool intersection( typename K::Segment_2 &result) const;
+    typename K::Point_2   intersection_point() const;
+    typename K::Segment_2 intersection_segment() const;
 protected:
     mutable bool                       _known;
     mutable Intersection_results       _result;
@@ -57,8 +58,7 @@ protected:
     mutable typename K::Vector_2           _dir;
     mutable typename K::Point_2            _isomin;
     mutable typename K::Point_2            _isomax;
-    mutable typename K::FT                     _min,
-                               _max;
+    mutable typename K::FT                     _min, _max;
 };
 
 template <class K>
@@ -91,16 +91,10 @@ intersection(const typename K::Ray_2 &ray,
     case is_t::NO_INTERSECTION:
     default:
         return Object();
-    case is_t::POINT: {
-        typename K::Point_2 ipt;
-        ispair.intersection(ipt);
-        return make_object(ipt);
-    }
-    case is_t::SEGMENT: {
-        typename K::Segment_2 iseg;
-        ispair.intersection(iseg);
-        return make_object(iseg);
-    }
+    case is_t::POINT:
+        return make_object(ispair.intersection_point());
+    case is_t::SEGMENT:
+        return make_object(ispair.intersection_segment());
     }
 }
 
@@ -113,27 +107,6 @@ intersection(const typename K::Iso_rectangle_2 &iso,
   return intersection(ray, iso, k);
 }
 
-
-template <class K>
-Ray_2_Iso_rectangle_2_pair<K>::Ray_2_Iso_rectangle_2_pair()
-{
-    _known = false;
-}
-
-template <class K>
-Ray_2_Iso_rectangle_2_pair<K>::
-Ray_2_Iso_rectangle_2_pair(
-        typename K::Ray_2 const *ray,
-        typename K::Iso_rectangle_2 const *iso)
-{
-    _known = false;
-    _isomin = (iso->min)();
-    _isomax = (iso->max)();
-    _ref_point = ray->source();
-    _dir = ray->direction().to_vector();
-    _min = (typename K::FT)(0);
-}
-
 template <class K>
 typename Ray_2_Iso_rectangle_2_pair<K>::Intersection_results
 Ray_2_Iso_rectangle_2_pair<K>::intersection_type() const
@@ -200,47 +173,32 @@ Ray_2_Iso_rectangle_2_pair<K>::intersection_type() const
 
 
 template <class K>
-bool Ray_2_Iso_rectangle_2_pair<K>::
-intersection(typename K::Segment_2 &seg) const
+typename K::Segment_2
+Ray_2_Iso_rectangle_2_pair<K>::intersection_segment() const
 {
-  typedef typename K::Segment_2 Segment_2; 
-  typename K::Construct_translated_point_2 translated_point;
-  typename K::Construct_scaled_vector_2 construct_scaled_vector;
+    typedef typename K::Segment_2 Segment_2; 
+    typename K::Construct_translated_point_2 translated_point;
+    typename K::Construct_scaled_vector_2 construct_scaled_vector;
     if (!_known)
         intersection_type();
-    if (_result != SEGMENT)
-        return false;
+    CGAL_kernel_assertion(_result == SEGMENT);
     typename K::Point_2 p1(translated_point(_ref_point, construct_scaled_vector(_dir,_min)));
     typename K::Point_2 p2(translated_point(_ref_point, construct_scaled_vector(_dir,_max)));
-    seg = Segment_2(p1, p2);
-    return true;
+    return Segment_2(p1, p2);
 }
 
-template <class K> bool Ray_2_Iso_rectangle_2_pair<K>::
-intersection(typename K::Point_2 &pt) const
-{
-  typedef typename K::Point_2 Point_2;
-  typename K::Construct_translated_point_2 translated_point;
-  typename K::Construct_scaled_vector_2 construct_scaled_vector;
-    if (!_known)
-        intersection_type();
-    if (_result != POINT)
-        return false;
-    pt = Point_2(translated_point(_ref_point, construct_scaled_vector(_dir, _min)));
-    return true;
-}
-
-
-
 template <class K>
-class Iso_rectangle_2_Ray_2_pair:
-          public Ray_2_Iso_rectangle_2_pair<K> {
-public:
-    Iso_rectangle_2_Ray_2_pair() {}
-    Iso_rectangle_2_Ray_2_pair(typename K::Iso_rectangle_2 const *rect,
-                               typename K::Ray_2 const *ray)
-                :Ray_2_Iso_rectangle_2_pair<K> (ray, rect){}
-};
+typename K::Point_2
+Ray_2_Iso_rectangle_2_pair<K>::intersection_point() const
+{
+    typedef typename K::Point_2 Point_2;
+    typename K::Construct_translated_point_2 translated_point;
+    typename K::Construct_scaled_vector_2 construct_scaled_vector;
+    if (!_known)
+        intersection_type();
+    CGAL_kernel_assertion(_result == POINT);
+    return Point_2(translated_point(_ref_point, construct_scaled_vector(_dir, _min)));
+}
 
 } // namespace CGALi
 
diff --git a/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h b/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
index df47e781bdc..61bf5e9b0be 100644
--- a/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
+++ b/Intersections_2/include/CGAL/Segment_2_Line_2_intersection.h
@@ -41,14 +41,14 @@ template <class K>
 class Segment_2_Line_2_pair {
 public:
     enum Intersection_results {NO_INTERSECTION, POINT, SEGMENT};
-    Segment_2_Line_2_pair() ;
     Segment_2_Line_2_pair(typename K::Segment_2 const *seg,
-                            typename K::Line_2 const *line);
+                          typename K::Line_2 const *line)
+      : _seg(seg), _line(line), _known(false) {}
 
     Intersection_results intersection_type() const;
 
-    bool                intersection(typename K::Point_2 &result) const;
-    bool                intersection(typename K::Segment_2 &result) const;
+    typename K::Point_2    intersection_point() const;
+    typename K::Segment_2  intersection_segment() const;
 protected:
     typename K::Segment_2 const*_seg;
     typename K::Line_2 const *  _line;
@@ -80,11 +80,8 @@ intersection(const typename K::Segment_2 &seg,
     case is_t::NO_INTERSECTION:
     default:
         return Object();
-    case is_t::POINT: {
-        typename K::Point_2 pt;
-        ispair.intersection(pt);
-        return make_object(pt);
-    }
+    case is_t::POINT:
+        return make_object(ispair.intersection_point());
     case is_t::SEGMENT:
         return make_object(seg);
     }
@@ -100,45 +97,18 @@ intersection(const typename K::Line_2 &line,
 }
 
 
-template <class K>
-class Line_2_Segment_2_pair: public Segment_2_Line_2_pair<K> {
-public:
-    Line_2_Segment_2_pair(
-            typename K::Line_2 const *line,
-            typename K::Segment_2 const *seg) :
-                                Segment_2_Line_2_pair<K>(seg, line) {}
-};
-
 template <class K>
 inline bool do_intersect(
     const typename K::Line_2 &p1,
     const typename K::Segment_2 &p2,
     const K&)
 {
-    typedef Line_2_Segment_2_pair<K> pair_t;
-    pair_t pair(&p1, &p2);
+    typedef Segment_2_Line_2_pair<K> pair_t;
+    pair_t pair(&p2, &p1);
     return pair.intersection_type() != pair_t::NO_INTERSECTION;
 }
 
 
-
-template <class K>
-Segment_2_Line_2_pair<K>::Segment_2_Line_2_pair()
-{
-    _seg = 0;
-    _line = 0;
-    _known = false;
-}
-
-template <class K>
-Segment_2_Line_2_pair<K>::Segment_2_Line_2_pair(
-    typename K::Segment_2 const *seg, typename K::Line_2 const *line)
-{
-    _seg = seg;
-    _line = line;
-    _known = false;
-}
-
 template <class K>
 typename Segment_2_Line_2_pair<K>::Intersection_results
 Segment_2_Line_2_pair<K>::intersection_type() const
@@ -166,27 +136,23 @@ Segment_2_Line_2_pair<K>::intersection_type() const
 }
 
 template <class K>
-bool
-Segment_2_Line_2_pair<K>::intersection(typename K::Point_2 &result) const
+typename K::Point_2
+Segment_2_Line_2_pair<K>::intersection_point() const
 {
     if (!_known)
         intersection_type();
-    if (_result != POINT)
-        return false;
-    result = _intersection_point;
-    return true;
+    CGAL_kernel_assertion(_result == POINT);
+    return _intersection_point;
 }
 
 template <class K>
-bool
-Segment_2_Line_2_pair<K>::intersection(typename K::Segment_2 &result) const
+typename K::Segment_2
+Segment_2_Line_2_pair<K>::intersection_segment() const
 {
     if (!_known)
         intersection_type();
-    if (_result != SEGMENT)
-        return false;
-    result = *_seg;
-    return true;
+    CGAL_kernel_assertion(_result == SEGMENT);
+    return *_seg;
 }
 
 } // namespace CGALi