diff --git a/lower-constraints.txt b/lower-constraints.txt
index 24e0e1b5b6..536e8b61ed 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -25,7 +25,7 @@ flake8==2.5.5
 future==0.16.0
 gitdb2==2.0.3
 GitPython==2.1.8
-greenlet==0.3.1
+greenlet==0.3.2
 hacking==0.11.0
 idna==2.6
 imagesize==1.0.0
diff --git a/requirements.txt b/requirements.txt
index 04f2af2c1c..d4c994af27 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,7 +4,7 @@
 
 dnspython>=1.15.0;python_version=='2.7' # http://www.dnspython.org/LICENSE
 eventlet>=0.25.0                        # MIT
-greenlet>=0.3.1
+greenlet>=0.3.2
 netifaces>=0.8,!=0.10.0,!=0.10.1
 PasteDeploy>=1.3.3
 lxml>=3.4.1
diff --git a/swift/proxy/controllers/obj.py b/swift/proxy/controllers/obj.py
index 8e6c475463..3015362c99 100644
--- a/swift/proxy/controllers/obj.py
+++ b/swift/proxy/controllers/obj.py
@@ -38,7 +38,7 @@ from hashlib import md5
 from swift import gettext_ as _
 
 from greenlet import GreenletExit
-from eventlet import GreenPile
+from eventlet import GreenPile, sleep
 from eventlet.queue import Queue
 from eventlet.timeout import Timeout
 
@@ -1066,6 +1066,7 @@ class ECAppIter(object):
         # executing the internal_parts_iters.
         if self.stashed_iter:
             self.stashed_iter.close()
+        sleep()  # Give the per-frag threads a chance to clean up
         for it in self.internal_parts_iters:
             close_if_possible(it)