diff --git a/Lib/subprocess.py b/Lib/subprocess.py
index dc639c9..6065594 100644
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -661,8 +661,10 @@
                 self.stdin.close()
             elif self.stdout:
                 stdout = self.stdout.read()
+                self.stdout.close()
             elif self.stderr:
                 stderr = self.stderr.read()
+                self.stderr.close()
             self.wait()
             return (stdout, stderr)
 
diff --git a/Lib/test/test_subprocess.py b/Lib/test/test_subprocess.py
index f31ce75..e7ba26f 100644
--- a/Lib/test/test_subprocess.py
+++ b/Lib/test/test_subprocess.py
@@ -287,14 +287,12 @@
                              stderr=subprocess.PIPE)
         (stdout, stderr) = p.communicate()
         self.assertEqual(stdout, None)
-        # When running with a pydebug build, the # of references is outputted
-        # to stderr, so just check if stderr at least started with "pinapple"
-        self.assert_(stderr.startswith("pineapple"))
+        self.assertEqual(remove_stderr_debug_decorations(stderr), "pineapple")
 
     def test_communicate(self):
         p = subprocess.Popen([sys.executable, "-c",
-                          'import sys,os;' \
-                          'sys.stderr.write("pineapple");' \
+                          'import sys,os;'
+                          'sys.stderr.write("pineapple");'
                           'sys.stdout.write(sys.stdin.read())'],
                          stdin=subprocess.PIPE,
                          stdout=subprocess.PIPE,
@@ -304,6 +302,22 @@
         self.assertEqual(remove_stderr_debug_decorations(stderr),
                          "pineapple")
 
+    # This test is Linux specific for simplicity to at least have
+    # some coverage.  It is not a platform specific bug.
+    if os.path.isdir('/proc/%d/fd' % os.getpid()):
+        # Test for the fd leak reported in http://bugs.python.org/issue2791.
+        def test_communicate_pipe_fd_leak(self):
+            fd_directory = '/proc/%d/fd' % os.getpid()
+            num_fds_before_popen = len(os.listdir(fd_directory))
+            p = subprocess.Popen([sys.executable, '-c', 'print()'],
+                                 stdout=subprocess.PIPE)
+            p.communicate()
+            num_fds_after_communicate = len(os.listdir(fd_directory))
+            del p
+            num_fds_after_destruction = len(os.listdir(fd_directory))
+            self.assertEqual(num_fds_before_popen, num_fds_after_destruction)
+            self.assertEqual(num_fds_before_popen, num_fds_after_communicate)
+
     def test_communicate_returns(self):
         # communicate() should return None if no redirection is active
         p = subprocess.Popen([sys.executable, "-c",