diff --git a/include/boost/geometry/iterators/box_iterator.hpp b/include/boost/geometry/iterators/box_iterator.hpp
index d3857f170..f177da610 100644
--- a/include/boost/geometry/iterators/box_iterator.hpp
+++ b/include/boost/geometry/iterators/box_iterator.hpp
@@ -32,7 +32,7 @@ struct box_iterator
     <
         box_iterator<Box>,
         typename point_type<Box>::type const,
-        boost::bidirectional_traversal_tag
+        boost::random_access_traversal_tag
     >
 {
     explicit inline box_iterator(Box const& box)
@@ -80,6 +80,11 @@ private:
         m_index--;
     }
 
+    inline difference_type distance_to(box_iterator<Box> const& other) const
+    {
+        return other.m_index - this->m_index;
+    }
+
     inline void init(Box const& box)
     {
         // asb -> lower_left, lower_right, upper_left, upper_right
diff --git a/include/boost/geometry/iterators/segment_range_iterator.hpp b/include/boost/geometry/iterators/segment_range_iterator.hpp
index e344ac493..396f5042c 100644
--- a/include/boost/geometry/iterators/segment_range_iterator.hpp
+++ b/include/boost/geometry/iterators/segment_range_iterator.hpp
@@ -32,7 +32,7 @@ struct segment_range_iterator
     <
         segment_range_iterator<Segment>,
         typename point_type<Segment>::type const,
-        boost::bidirectional_traversal_tag
+        boost::random_access_traversal_tag
     >
 {
     // Default constructor is required to check concept of Range
@@ -90,13 +90,18 @@ private:
         m_index--;
     }
 
+    inline difference_type distance_to(segment_range_iterator<Segment> const& other) const
+    {
+        return other.m_index - this->m_index;
+    }
+
     inline void init(Segment const& segment)
     {
         assign_point_from_index<0>(segment, m_points[0]);
         assign_point_from_index<1>(segment, m_points[1]);
     }
 
-    // We HAVE TO copy the points, because a segment does not need 
+    // We HAVE TO copy the points, because a segment does not need
     // to consist of two points,
     // and we are expected to return a point here
     point_type m_points[2];
diff --git a/include/boost/geometry/ranges/box_range.hpp b/include/boost/geometry/ranges/box_range.hpp
index 7c3ffe365..fc81c0495 100644
--- a/include/boost/geometry/ranges/box_range.hpp
+++ b/include/boost/geometry/ranges/box_range.hpp
@@ -43,7 +43,7 @@ private :
 };
 
 
-// All box ranges can be handled as linestrings
+// All box ranges can be handled as rings
 namespace traits
 {
     template<typename Box>
diff --git a/test/ranges/box_range.cpp b/test/ranges/box_range.cpp
index 07a8d04f8..59d47e803 100644
--- a/test/ranges/box_range.cpp
+++ b/test/ranges/box_range.cpp
@@ -46,6 +46,12 @@ void test_geometry(std::string const& wkt, std::string const& expected)
         it--;
         // Not verified further, same as segment
     }
+
+    {
+        // Check random access behaviour
+        int const n = boost::size(range);
+        BOOST_CHECK_EQUAL(n, 5);
+    }
 }
 
 
diff --git a/test/ranges/segment_range.cpp b/test/ranges/segment_range.cpp
index deb4ccef4..7285b702f 100644
--- a/test/ranges/segment_range.cpp
+++ b/test/ranges/segment_range.cpp
@@ -52,6 +52,12 @@ void test_geometry(std::string const& wkt, std::string const& expected)
         out << " " << boost::geometry::get<0>(*it2) << boost::geometry::get<1>(*it2);
         BOOST_CHECK_EQUAL(out.str(), expected);
     }
+
+    {
+        // Check random access behaviour
+        int const n = boost::size(range);
+        BOOST_CHECK_EQUAL(n, 2);
+    }
 }