diff --git a/swift/common/middleware/copy.py b/swift/common/middleware/copy.py
index 0ee5315a60..f6953ab2a6 100644
--- a/swift/common/middleware/copy.py
+++ b/swift/common/middleware/copy.py
@@ -413,9 +413,11 @@ class ServerSideCopyMiddleware(object):
             # which currently only happens because there are more than
             # CONTAINER_LISTING_LIMIT segments in a segmented object. In
             # this case, we're going to refuse to do the server-side copy.
+            close_if_possible(source_resp.app_iter)
             return HTTPRequestEntityTooLarge(request=req)
 
         if source_resp.content_length > MAX_FILE_SIZE:
+            close_if_possible(source_resp.app_iter)
             return HTTPRequestEntityTooLarge(request=req)
 
         return source_resp
@@ -459,7 +461,6 @@ class ServerSideCopyMiddleware(object):
         ssc_ctx = ServerSideCopyWebContext(self.app, self.logger)
         source_resp = self._get_source_object(ssc_ctx, source_path, req)
         if source_resp.status_int >= HTTP_MULTIPLE_CHOICES:
-            close_if_possible(source_resp.app_iter)
             return source_resp(source_resp.environ, start_response)
 
         # Create a new Request object based on the original request instance.
diff --git a/test/unit/common/middleware/test_copy.py b/test/unit/common/middleware/test_copy.py
index 08d9acdfb1..bbf74bbc1b 100644
--- a/test/unit/common/middleware/test_copy.py
+++ b/test/unit/common/middleware/test_copy.py
@@ -27,6 +27,7 @@ from swift.common import swob
 from swift.common.middleware import copy
 from swift.common.storage_policy import POLICIES
 from swift.common.swob import Request, HTTPException
+from swift.common.utils import closing_if_possible
 from test.unit import patch_policies, debug_logger, FakeMemcache, FakeRing
 from test.unit.common.middleware.helpers import FakeSwift
 from test.unit.proxy.controllers.test_obj import set_http_connect, \
@@ -97,6 +98,9 @@ class TestServerSideCopyMiddleware(unittest.TestCase):
         })(self.app)
         self.ssc.logger = self.app.logger
 
+    def tearDown(self):
+        self.assertEqual(self.app.unclosed_requests, {})
+
     def call_app(self, req, app=None, expect_exception=False):
         if app is None:
             app = self.app
@@ -122,8 +126,10 @@ class TestServerSideCopyMiddleware(unittest.TestCase):
         body = ''
         caught_exc = None
         try:
-            for chunk in body_iter:
-                body += chunk
+            # appease the close-checker
+            with closing_if_possible(body_iter):
+                for chunk in body_iter:
+                    body += chunk
         except Exception as exc:
             if expect_exception:
                 caught_exc = exc