diff --git a/Lib/subprocess.py b/Lib/subprocess.py
index 1f6eb63..0496b44 100644
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -50,6 +50,7 @@
 import sys
 import threading
 import warnings
+import contextlib
 from time import monotonic as _time
 
 
@@ -1072,28 +1073,28 @@
         # self._devnull is not always defined.
         devnull_fd = getattr(self, '_devnull', None)
 
-        if _mswindows:
-            if p2cread != -1:
-                p2cread.Close()
-            if c2pwrite != -1:
-                c2pwrite.Close()
-            if errwrite != -1:
-                errwrite.Close()
-        else:
-            if p2cread != -1 and p2cwrite != -1 and p2cread != devnull_fd:
-                os.close(p2cread)
-            if c2pwrite != -1 and c2pread != -1 and c2pwrite != devnull_fd:
-                os.close(c2pwrite)
-            if errwrite != -1 and errread != -1 and errwrite != devnull_fd:
-                os.close(errwrite)
+        with contextlib.ExitStack() as stack:
+            if _mswindows:
+                if p2cread != -1:
+                    stack.callback(p2cread.Close)
+                if c2pwrite != -1:
+                    stack.callback(c2pwrite.Close)
+                if errwrite != -1:
+                    stack.callback(errwrite.Close)
+            else:
+                if p2cread != -1 and p2cwrite != -1 and p2cread != devnull_fd:
+                    stack.callback(os.close, p2cread)
+                if c2pwrite != -1 and c2pread != -1 and c2pwrite != devnull_fd:
+                    stack.callback(os.close, c2pwrite)
+                if errwrite != -1 and errread != -1 and errwrite != devnull_fd:
+                    stack.callback(os.close, errwrite)
 
-        if devnull_fd is not None:
-            os.close(devnull_fd)
+            if devnull_fd is not None:
+                stack.callback(os.close, devnull_fd)
 
         # Prevent a double close of these handles/fds from __init__ on error.
         self._closed_child_pipe_fds = True
 
-
     if _mswindows:
         #
         # Windows methods
diff --git a/Misc/NEWS.d/next/Library/2019-01-29-17-24-52.bpo-35537.Q0ktFC.rst b/Misc/NEWS.d/next/Library/2019-01-29-17-24-52.bpo-35537.Q0ktFC.rst
new file mode 100644
index 0000000..2a9588e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-01-29-17-24-52.bpo-35537.Q0ktFC.rst
@@ -0,0 +1,4 @@
+An ExitStack is now used internally within subprocess.POpen to clean up pipe
+file handles. No behavior change in normal operation. But if closing one
+handle were ever to cause an exception, the others will now be closed
+instead of leaked.  (patch by Giampaolo Rodola)