diff --git a/include/fmt/format.h b/include/fmt/format.h
index 685474f0..11a0669b 100644
--- a/include/fmt/format.h
+++ b/include/fmt/format.h
@@ -738,8 +738,9 @@ using is_double_double = bool_constant<std::numeric_limits<T>::digits == 106>;
 #endif
 
 // An allocator that uses malloc/free to allow removing dependency on the C++
-// standard libary runtime.
-template <typename T> struct allocator {
+// standard libary runtime. std::decay is used for back_inserter to be found by
+// ADL when applied to memory_buffer.
+template <typename T> struct allocator : private std::decay<void> {
   using value_type = T;
 
   T* allocate(size_t n) {
diff --git a/test/format-test.cc b/test/format-test.cc
index e630ab0f..c0e1ea68 100644
--- a/test/format-test.cc
+++ b/test/format-test.cc
@@ -481,6 +481,12 @@ TEST(memory_buffer_test, max_size_allocator_overflow) {
   EXPECT_THROW(buffer.resize(161), std::exception);
 }
 
+TEST(memory_buffer_test, back_insert_iterator) {
+  fmt::memory_buffer buf;
+  using iterator = decltype(std::back_inserter(buf));
+  EXPECT_TRUE(fmt::detail::is_back_insert_iterator<iterator>::value);
+}
+
 TEST(format_test, digits2_alignment) {
   auto p =
       fmt::detail::bit_cast<fmt::detail::uintptr_t>(fmt::detail::digits2(0));