diff --git a/include/boost/unordered_map.hpp b/include/boost/unordered_map.hpp
index abb49e04..7b9af025 100644
--- a/include/boost/unordered_map.hpp
+++ b/include/boost/unordered_map.hpp
@@ -158,47 +158,32 @@ namespace boost
                     base.insert(obj));
         }
 
-        iterator insert(iterator hint, const value_type& obj)
+        iterator insert(const_iterator hint, const value_type& obj)
         {
             return iterator(base.insert(get(hint), obj));
         }
 
-        const_iterator insert(const_iterator hint, const value_type& obj)
-        {
-            return const_iterator(base.insert(get(hint), obj));
-        }
-
         template <class InputIterator>
             void insert(InputIterator first, InputIterator last)
         {
             base.insert(first, last);
         }
 
-        iterator erase(iterator position)
+        iterator erase(const_iterator position)
         {
             return iterator(base.erase(get(position)));
         }
 
-        const_iterator erase(const_iterator position)
-        {
-            return const_iterator(base.erase(get(position)));
-        }
-
         size_type erase(const key_type& k)
         {
             return base.erase(k);
         }
 
-        iterator erase(iterator first, iterator last)
+        iterator erase(const_iterator first, const_iterator last)
         {
             return iterator(base.erase(get(first), get(last)));
         }
 
-        const_iterator erase(const_iterator first, const_iterator last)
-        {
-            return const_iterator(base.erase(get(first), get(last)));
-        }
-
         void clear()
         {
             base.clear();
@@ -477,47 +462,32 @@ namespace boost
             return iterator(base.insert(obj));
         }
 
-        iterator insert(iterator hint, const value_type& obj)
+        iterator insert(const_iterator hint, const value_type& obj)
         {
             return iterator(base.insert(get(hint), obj));
         }
 
-        const_iterator insert(const_iterator hint, const value_type& obj)
-        {
-            return const_iterator(base.insert(get(hint), obj));
-        }
-
         template <class InputIterator>
             void insert(InputIterator first, InputIterator last)
         {
             base.insert(first, last);
         }
 
-        iterator erase(iterator position)
+        iterator erase(const_iterator position)
         {
             return iterator(base.erase(get(position)));
         }
 
-        const_iterator erase(const_iterator position)
-        {
-            return const_iterator(base.erase(get(position)));
-        }
-
         size_type erase(const key_type& k)
         {
             return base.erase(k);
         }
 
-        iterator erase(iterator first, iterator last)
+        iterator erase(const_iterator first, const_iterator last)
         {
             return iterator(base.erase(get(first), get(last)));
         }
 
-        const_iterator erase(const_iterator first, const_iterator last)
-        {
-            return const_iterator(base.erase(get(first), get(last)));
-        }
-
         void clear()
         {
             base.clear();
diff --git a/include/boost/unordered_set.hpp b/include/boost/unordered_set.hpp
index cb7be821..15c20c15 100644
--- a/include/boost/unordered_set.hpp
+++ b/include/boost/unordered_set.hpp
@@ -155,9 +155,9 @@ namespace boost
                     base.insert(obj));
         }
 
-        const_iterator insert(const_iterator hint, const value_type& obj)
+        iterator insert(const_iterator hint, const value_type& obj)
         {
-            return const_iterator(base.insert(get(hint), obj));
+            return iterator(base.insert(get(hint), obj));
         }
 
         template <class InputIterator>
@@ -166,9 +166,9 @@ namespace boost
             base.insert(first, last);
         }
 
-        const_iterator erase(const_iterator position)
+        iterator erase(const_iterator position)
         {
-            return const_iterator(base.erase(get(position)));
+            return iterator(base.erase(get(position)));
         }
 
         size_type erase(const key_type& k)
@@ -176,9 +176,9 @@ namespace boost
             return base.erase(k);
         }
 
-        const_iterator erase(const_iterator first, const_iterator last)
+        iterator erase(const_iterator first, const_iterator last)
         {
-            return const_iterator(base.erase(get(first), get(last)));
+            return iterator(base.erase(get(first), get(last)));
         }
 
         void clear()
@@ -439,9 +439,9 @@ namespace boost
             return iterator(base.insert(obj));
         }
 
-        const_iterator insert(const_iterator hint, const value_type& obj)
+        iterator insert(const_iterator hint, const value_type& obj)
         {
-            return const_iterator(base.insert(get(hint), obj));
+            return iterator(base.insert(get(hint), obj));
         }
 
         template <class InputIterator>
@@ -450,9 +450,9 @@ namespace boost
             base.insert(first, last);
         }
 
-        const_iterator erase(const_iterator position)
+        iterator erase(const_iterator position)
         {
-            return const_iterator(base.erase(get(position)));
+            return iterator(base.erase(get(position)));
         }
 
         size_type erase(const key_type& k)
@@ -460,9 +460,9 @@ namespace boost
             return base.erase(k);
         }
 
-        const_iterator erase(const_iterator first, const_iterator last)
+        iterator erase(const_iterator first, const_iterator last)
         {
-            return const_iterator(base.erase(get(first), get(last)));
+            return iterator(base.erase(get(first), get(last)));
         }
 
         void clear()
diff --git a/test/objects/minimal.hpp b/test/objects/minimal.hpp
index 3fd48da0..63863318 100644
--- a/test/objects/minimal.hpp
+++ b/test/objects/minimal.hpp
@@ -125,9 +125,9 @@ namespace minimal
     {
         friend class allocator<T>;
 
-        T* ptr_;
+        T const* ptr_;
 
-        const_ptr(T* ptr) : ptr_(ptr) {}
+        const_ptr(T const* ptr) : ptr_(ptr) {}
     public:
         const_ptr() : ptr_(0) {}
         const_ptr(ptr<T> const& x) : ptr_(x.ptr_) {}
@@ -135,12 +135,12 @@ namespace minimal
         typedef void (const_ptr::*bool_type)() const;
         void this_type_does_not_support_comparisons() const {}
 
-        T& operator*() const { return *ptr_; }
-        T* operator->() const { return ptr_; }
+        T const& operator*() const { return *ptr_; }
+        T const* operator->() const { return ptr_; }
         const_ptr& operator++() { ++ptr_; return *this; }
         const_ptr operator++(int) { const_ptr tmp(*this); ++ptr_; return tmp; }
         const_ptr operator+(int s) const { return const_ptr(ptr_ + s); }
-        T& operator[](int s) const { return ptr_[s]; }
+        T const& operator[](int s) const { return ptr_[s]; }
         bool operator!() const { return !ptr_; }
 
         operator bool_type() const {
diff --git a/test/unordered/compile_tests.cpp b/test/unordered/compile_tests.cpp
index 9573b2de..7a0ba38f 100644
--- a/test/unordered/compile_tests.cpp
+++ b/test/unordered/compile_tests.cpp
@@ -144,10 +144,8 @@ void unordered_test(X&, Key& k, T& t, Hash& hf, Pred& eq)
     test::check_return_type<hasher>::equals(b.hash_function());
     test::check_return_type<key_equal>::equals(b.key_eq());
 
-    iterator q = a.begin();
-    const_iterator r = a.begin();
+    const_iterator q = a.cbegin();
     test::check_return_type<iterator>::equals(a.insert(q, t));
-    test::check_return_type<const_iterator>::equals(a.insert(r, t));
 
     // TODO: void return?
     a.insert(i, j);
@@ -156,23 +154,13 @@ void unordered_test(X&, Key& k, T& t, Hash& hf, Pred& eq)
     BOOST_TEST(a.empty());
     if(a.empty()) {
         a.insert(t);
-        q = a.begin();
+        q = a.cbegin();
         test::check_return_type<iterator>::equals(a.erase(q));
     }
 
-    BOOST_TEST(a.empty());
-    if(a.empty()) {
-        a.insert(t);
-        r = a.begin();
-        test::check_return_type<const_iterator>::equals(a.erase(r));
-    }
-
-    iterator q1 = a.begin(), q2 = a.end();
+    const_iterator q1 = a.cbegin(), q2 = a.cend();
     test::check_return_type<iterator>::equals(a.erase(q1, q2));
 
-    const_iterator r1 = a.begin(), r2 = a.end();
-    test::check_return_type<const_iterator>::equals(a.erase(r1, r2));
-
     // TODO: void return?
     a.clear();