diff --git a/doc/mp11/algorithm.adoc b/doc/mp11/algorithm.adoc
index fa0dc50..5c6b22a 100644
--- a/doc/mp11/algorithm.adoc
+++ b/doc/mp11/algorithm.adoc
@@ -504,7 +504,13 @@ Like `mp_nth_element`, but takes a quoted metafunction.
 
 `mp_min_element<L, P>` returns the minimal element of the list `L` according to the ordering `mp_to_bool<P<T, U>>`.
 
-It's equivalent to `mp_fold<mp_rest<L>, mp_first<L>, Q>`, where `Q<T, U>` returns `mp_if<P<T, U>, T, U>`.
+It's equivalent to `mp_fold<mp_rest<L>, mp_first<L>, F>`, where `F<T, U>` returns `mp_if<P<T, U>, T, U>`.
+
+## mp_min_element_q<L, Q>
+
+    template<class L, class Q> using mp_min_element_q = mp_min_element<L, Q::template fn>;
+
+As `mp_min_element`, but takes a quoted metafunction.
 
 ## mp_max_element<L, P>
 
@@ -512,7 +518,13 @@ It's equivalent to `mp_fold<mp_rest<L>, mp_first<L>, Q>`, where `Q<T, U>` return
 
 `mp_max_element<L, P>` returns the maximal element of the list `L` according to the ordering `mp_to_bool<P<T, U>>`.
 
-It's equivalent to `mp_fold<mp_rest<L>, mp_first<L>, Q>`, where `Q<T, U>` returns `mp_if<P<U, T>, T, U>`.
+It's equivalent to `mp_fold<mp_rest<L>, mp_first<L>, F>`, where `F<T, U>` returns `mp_if<P<U, T>, T, U>`.
+
+## mp_max_element_q<L, Q>
+
+    template<class L, class Q> using mp_max_element_q = mp_max_element<L, Q::template fn>;
+
+As `mp_max_element`, but takes a quoted metafunction.
 
 ## mp_find<L, V>
 
diff --git a/include/boost/mp11/detail/mp_min_element.hpp b/include/boost/mp11/detail/mp_min_element.hpp
index 3b4f274..55c21ac 100644
--- a/include/boost/mp11/detail/mp_min_element.hpp
+++ b/include/boost/mp11/detail/mp_min_element.hpp
@@ -29,6 +29,7 @@ template<template<class...> class P> struct select_min
 } // namespace detail
 
 template<class L, template<class...> class P> using mp_min_element = mp_fold_q<mp_rest<L>, mp_first<L>, detail::select_min<P>>;
+template<class L, class Q> using mp_min_element_q = mp_min_element<L, Q::template fn>;
 
 // mp_max_element<L, P>
 namespace detail
@@ -42,6 +43,7 @@ template<template<class...> class P> struct select_max
 } // namespace detail
 
 template<class L, template<class...> class P> using mp_max_element = mp_fold_q<mp_rest<L>, mp_first<L>, detail::select_max<P>>;
+template<class L, class Q> using mp_max_element_q = mp_max_element<L, Q::template fn>;
 
 } // namespace mp11
 } // namespace boost
diff --git a/test/Jamfile b/test/Jamfile
index ba4a16d..ed2e96c 100644
--- a/test/Jamfile
+++ b/test/Jamfile
@@ -85,7 +85,9 @@ run mp_with_index.cpp ;
 run mp_with_index_cx.cpp ;
 run mp_from_sequence.cpp ;
 run mp_min_element.cpp ;
+run mp_min_element_q.cpp ;
 run mp_max_element.cpp ;
+run mp_max_element_q.cpp ;
 run mp_nth_element.cpp ;
 run mp_nth_element_q.cpp ;
 
diff --git a/test/mp_max_element_q.cpp b/test/mp_max_element_q.cpp
new file mode 100644
index 0000000..36a79c4
--- /dev/null
+++ b/test/mp_max_element_q.cpp
@@ -0,0 +1,58 @@
+
+// Copyright 2017 Peter Dimov.
+//
+// Distributed under the Boost Software License, Version 1.0.
+//
+// See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+
+
+#include <boost/mp11/algorithm.hpp>
+#include <boost/mp11/list.hpp>
+#include <boost/mp11/integral.hpp>
+#include <boost/core/lightweight_test_trait.hpp>
+#include <type_traits>
+#include <tuple>
+
+using boost::mp11::mp_bool;
+
+struct Q_sizeof_less
+{
+    template<class T, class U> using fn = mp_bool<(sizeof(T) < sizeof(U))>;
+};
+
+int main()
+{
+    using boost::mp11::mp_list;
+    using boost::mp11::mp_max_element_q;
+
+    {
+        using L1 = mp_list<void>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_max_element_q<L1, Q_sizeof_less>, void>));
+
+        using L2 = mp_list<char[2], char[4], char[3], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_max_element_q<L2, Q_sizeof_less>, char[4]>));
+
+        using L3 = mp_list<char[2], char[4], char[2], char[3], char[1], char[2], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_max_element_q<L3, Q_sizeof_less>, char[4]>));
+    }
+
+    {
+        using L1 = std::tuple<void>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_max_element_q<L1, Q_sizeof_less>, void>));
+
+        using L2 = std::tuple<char[2], char[4], char[3], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_max_element_q<L2, Q_sizeof_less>, char[4]>));
+
+        using L3 = std::tuple<char[2], char[4], char[2], char[3], char[1], char[2], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_max_element_q<L3, Q_sizeof_less>, char[4]>));
+    }
+
+    return boost::report_errors();
+}
diff --git a/test/mp_min_element_q.cpp b/test/mp_min_element_q.cpp
new file mode 100644
index 0000000..b1a0920
--- /dev/null
+++ b/test/mp_min_element_q.cpp
@@ -0,0 +1,58 @@
+
+// Copyright 2017 Peter Dimov.
+//
+// Distributed under the Boost Software License, Version 1.0.
+//
+// See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+
+
+#include <boost/mp11/algorithm.hpp>
+#include <boost/mp11/list.hpp>
+#include <boost/mp11/integral.hpp>
+#include <boost/core/lightweight_test_trait.hpp>
+#include <type_traits>
+#include <tuple>
+
+using boost::mp11::mp_bool;
+
+struct Q_sizeof_less
+{
+    template<class T, class U> using fn = mp_bool<(sizeof(T) < sizeof(U))>;
+};
+
+int main()
+{
+    using boost::mp11::mp_list;
+    using boost::mp11::mp_min_element_q;
+
+    {
+        using L1 = mp_list<void>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_min_element_q<L1, Q_sizeof_less>, void>));
+
+        using L2 = mp_list<char[2], char[4], char[3], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_min_element_q<L2, Q_sizeof_less>, char[1]>));
+
+        using L3 = mp_list<char[2], char[4], char[2], char[3], char[1], char[2], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_min_element_q<L3, Q_sizeof_less>, char[1]>));
+    }
+
+    {
+        using L1 = std::tuple<void>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_min_element_q<L1, Q_sizeof_less>, void>));
+
+        using L2 = std::tuple<char[2], char[4], char[3], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_min_element_q<L2, Q_sizeof_less>, char[1]>));
+
+        using L3 = std::tuple<char[2], char[4], char[2], char[3], char[1], char[2], char[1]>;
+
+        BOOST_TEST_TRAIT_TRUE((std::is_same<mp_min_element_q<L3, Q_sizeof_less>, char[1]>));
+    }
+
+    return boost::report_errors();
+}