diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 786e36f6a..6d25fa57d 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -1353,7 +1353,7 @@ template <typename Iterator, typename Sentinel, bool KeyIterator, return_value_p
 struct iterator_state {
     Iterator it;
     Sentinel end;
-    bool first;
+    bool first_or_done;
 };
 
 NAMESPACE_END(detail)
@@ -1374,17 +1374,19 @@ iterator make_iterator(Iterator first, Sentinel last, Extra &&... extra) {
         class_<state>(handle(), "iterator")
             .def("__iter__", [](state &s) -> state& { return s; })
             .def("__next__", [](state &s) -> ValueType {
-                if (!s.first)
+                if (!s.first_or_done)
                     ++s.it;
                 else
-                    s.first = false;
-                if (s.it == s.end)
+                    s.first_or_done = false;
+                if (s.it == s.end) {
+                    s.first_or_done = true;
                     throw stop_iteration();
+                }
                 return *s.it;
             }, std::forward<Extra>(extra)..., Policy);
     }
 
-    return (iterator) cast(state { first, last, true });
+    return cast(state{first, last, true});
 }
 
 /// Makes an python iterator over the keys (`.first`) of a iterator over pairs from a
@@ -1401,17 +1403,19 @@ iterator make_key_iterator(Iterator first, Sentinel last, Extra &&... extra) {
         class_<state>(handle(), "iterator")
             .def("__iter__", [](state &s) -> state& { return s; })
             .def("__next__", [](state &s) -> KeyType {
-                if (!s.first)
+                if (!s.first_or_done)
                     ++s.it;
                 else
-                    s.first = false;
-                if (s.it == s.end)
+                    s.first_or_done = false;
+                if (s.it == s.end) {
+                    s.first_or_done = true;
                     throw stop_iteration();
+                }
                 return (*s.it).first;
             }, std::forward<Extra>(extra)..., Policy);
     }
 
-    return (iterator) cast(state { first, last, true });
+    return cast(state{first, last, true});
 }
 
 /// Makes an iterator over values of an stl container or other container supporting
diff --git a/tests/test_sequences_and_iterators.py b/tests/test_sequences_and_iterators.py
index 30b6aaf4b..e04c579dd 100644
--- a/tests/test_sequences_and_iterators.py
+++ b/tests/test_sequences_and_iterators.py
@@ -21,6 +21,17 @@ def test_generalized_iterators():
     assert list(IntPairs([(1, 2), (2, 0), (0, 3), (4, 5)]).nonzero_keys()) == [1]
     assert list(IntPairs([(0, 3), (1, 2), (3, 4)]).nonzero_keys()) == []
 
+    # __next__ must continue to raise StopIteration
+    it = IntPairs([(0, 0)]).nonzero()
+    for _ in range(3):
+        with pytest.raises(StopIteration):
+            next(it)
+
+    it = IntPairs([(0, 0)]).nonzero_keys()
+    for _ in range(3):
+        with pytest.raises(StopIteration):
+            next(it)
+
 
 def test_sequence():
     from pybind11_tests import ConstructorStats
@@ -45,6 +56,12 @@ def test_sequence():
     rev2 = s[::-1]
     assert cstats.values() == ['of size', '5']
 
+    it = iter(Sequence(0))
+    for _ in range(3):  # __next__ must continue to raise StopIteration
+        with pytest.raises(StopIteration):
+            next(it)
+    assert cstats.values() == ['of size', '0']
+
     expected = [0, 56.78, 0, 0, 12.34]
     assert allclose(rev, expected)
     assert allclose(rev2, expected)
@@ -55,6 +72,8 @@ def test_sequence():
 
     assert allclose(rev, [2, 56.78, 2, 0, 2])
 
+    assert cstats.alive() == 4
+    del it
     assert cstats.alive() == 3
     del s
     assert cstats.alive() == 2
@@ -90,6 +109,11 @@ def test_map_iterator():
     for k, v in m.items():
         assert v == expected[k]
 
+    it = iter(StringMap({}))
+    for _ in range(3):  # __next__ must continue to raise StopIteration
+        with pytest.raises(StopIteration):
+            next(it)
+
 
 def test_python_iterator_in_cpp():
     import pybind11_tests.sequences_and_iterators as m