Index: Lib/unittest.py
===================================================================
--- Lib/unittest.py	(revision 87572)
+++ Lib/unittest.py	(working copy)
@@ -1464,7 +1464,9 @@
     It prints out the names of tests as they are run, errors as they
     occur, and a summary of the results at the end of the test run.
     """
-    def __init__(self, stream=sys.stderr, descriptions=1, verbosity=1):
+    def __init__(self, stream=None, descriptions=1, verbosity=1):
+        if stream is None:
+            stream = sys.stderr
         self.stream = _WritelnDecorator(stream)
         self.descriptions = descriptions
         self.verbosity = verbosity
Index: Lib/test/test_unittest.py
===================================================================
--- Lib/test/test_unittest.py	(revision 87572)
+++ Lib/test/test_unittest.py	(working copy)
@@ -7,6 +7,7 @@
 """
 
 import re
+import sys
 from test import support
 import unittest
 from unittest import TestCase, TestProgram
@@ -3346,7 +3347,21 @@
         expected = ['startTestRun', 'stopTestRun']
         self.assertEqual(events, expected)
 
+    def testStdErrLookedUpAtInstantiationTime(self):
+        # see issue 10786
+        old_stderr = sys.stderr
+        f = io.StringIO()
+        sys.stderr = f
+        runner = unittest.TextTestRunner()
+        self.assertTrue(runner.stream.stream is f)
+        sys.stderr = old_stderr
 
+    def testSpecifiedStreamUsed(self):
+        # see issue 10786
+        f = io.StringIO()
+        runner = unittest.TextTestRunner(f)
+        self.assertTrue(runner.stream.stream is f)
+
 ######################################################################
 ## Main
 ######################################################################
@@ -3355,7 +3370,7 @@
     support.run_unittest(Test_TestCase, Test_TestLoader,
         Test_TestSuite, Test_TestResult, Test_FunctionTestCase,
         Test_TestSkipping, Test_Assertions, TestLongMessage,
-        Test_TestProgram, TestCleanUp)
+        Test_TestProgram, TestCleanUp, Test_TextTestRunner)
 
 if __name__ == "__main__":
     test_main()