diff --git a/Lib/test/test_subprocess.py b/Lib/test/test_subprocess.py
--- a/Lib/test/test_subprocess.py
+++ b/Lib/test/test_subprocess.py
@@ -150,16 +150,29 @@
         self.assertEqual(p.stdin, None)
 
     def test_stdout_none(self):
-        # .stdout is None when not redirected
-        p = subprocess.Popen([sys.executable, "-c",
-                             'print "    this bit of output is from a '
-                             'test of stdout in a different '
-                             'process ..."'],
-                             stdin=subprocess.PIPE, stderr=subprocess.PIPE)
+        # .stdout is None when not redirected, and the child's stdout will
+        # be inherited from the parent.  In order to test this we run a
+        # subprocess in a subprocess:
+        # this_test
+        #   \-- subprocess created by this test (parent)
+        #          \-- subprocess created by the parent subprocess (child)
+        # The parent doesn't specify stdout, so the child will use the
+        # parent's stdout.  This test checks that the message printed by the
+        # child goes to the parent stdout.  The parent also checks that the
+        # child's stdout is None.  See #11963.
+        code = ('import sys; from subprocess import Popen, PIPE;'
+                'p = Popen([sys.executable, "-c", "print \'test_stdout_none\'"],'
+                '          stdin=PIPE, stderr=PIPE);'
+                'p.wait(); assert p.stdout == None;')
+        PIPE = subprocess.PIPE
+        p = subprocess.Popen([sys.executable, "-c", code],
+                             stdout=PIPE, stdin=PIPE, stderr=PIPE)
         self.addCleanup(p.stdin.close)
+        self.addCleanup(p.stdout.close)
         self.addCleanup(p.stderr.close)
-        p.wait()
-        self.assertEqual(p.stdout, None)
+        out, err = p.communicate()
+        self.assertEqual(p.returncode, 0)
+        self.assertEqual(out, 'test_stdout_none\n')
 
     def test_stderr_none(self):
         # .stderr is None when not redirected
@@ -308,9 +321,21 @@
 
     def test_stdout_filedes_of_stdout(self):
         # stdout is set to 1 (#1531862).
-        cmd = r"import sys, os; sys.exit(os.write(sys.stdout.fileno(), '.\n'))"
-        rc = subprocess.call([sys.executable, "-c", cmd], stdout=1)
-        self.assertEqual(rc, 2)
+        # To avoid printing the '.\n' on stdout, we do something similar to
+        # test_stdout_none (see above).  The parent subprocess calls the child
+        # subprocess passing stdout=1, and this tests uses stdout=PIPE in
+        # order to capture and check the output of the parent. See #11963.
+        code = ('import sys, subprocess; '
+                'rc = subprocess.call([sys.executable, "-c", '
+                '    "import os, sys; sys.exit(os.write(sys.stdout.fileno(), '
+                     '\'.\\\\n\'))"], stdout=1); '
+                'assert rc == 2')
+        PIPE = subprocess.PIPE
+        p = subprocess.Popen([sys.executable, "-c", code],
+                             stdout=PIPE, stdin=PIPE, stderr=PIPE)
+        out, err = p.communicate()
+        self.assertEqual(p.returncode, 0)
+        self.assertEqual(out, '.\n')
 
     def test_cwd(self):
         tmpdir = tempfile.gettempdir()