diff --git a/swift/common/utils.py b/swift/common/utils.py
index 055d10e3c6..792f7f5bc1 100644
--- a/swift/common/utils.py
+++ b/swift/common/utils.py
@@ -3821,8 +3821,9 @@ def document_iters_to_http_response_body(ranges_iter, boundary, multipart,
         # so if that finally block fires before we read response_body_iter,
         # there's nothing there.
         def string_along(useful_iter, useless_iter_iter, logger):
-            for x in useful_iter:
-                yield x
+            with closing_if_possible(useful_iter):
+                for x in useful_iter:
+                    yield x
 
             try:
                 next(useless_iter_iter)
diff --git a/test/unit/common/test_utils.py b/test/unit/common/test_utils.py
index bfa7ddb072..813256bded 100644
--- a/test/unit/common/test_utils.py
+++ b/test/unit/common/test_utils.py
@@ -5703,6 +5703,28 @@ class TestDocumentItersToHTTPResponseBody(unittest.TestCase):
             part2 + "\r\n" +
             "--boundaryboundary--"))
 
+    def test_closed_part_iterator(self):
+        print('test')
+        useful_iter_mock = mock.MagicMock()
+        useful_iter_mock.__iter__.return_value = ['']
+        body_iter = utils.document_iters_to_http_response_body(
+            iter([{'part_iter': useful_iter_mock}]), 'dontcare',
+            multipart=False, logger=FakeLogger())
+        body = ''
+        for s in body_iter:
+            body += s
+        self.assertEqual(body, '')
+        useful_iter_mock.close.assert_called_once_with()
+
+        # Calling "close" on the mock will now raise an AttributeError
+        del useful_iter_mock.close
+        body_iter = utils.document_iters_to_http_response_body(
+            iter([{'part_iter': useful_iter_mock}]), 'dontcare',
+            multipart=False, logger=FakeLogger())
+        body = ''
+        for s in body_iter:
+            body += s
+
 
 class TestPairs(unittest.TestCase):
     def test_pairs(self):