diff --git a/Lib/unittest/runner.py b/Lib/unittest/runner.py
index c5e4258..10c4778 100644
--- a/Lib/unittest/runner.py
+++ b/Lib/unittest/runner.py
@@ -125,8 +125,10 @@
     """
     resultclass = TextTestResult
 
-    def __init__(self, stream=sys.stderr, descriptions=True, verbosity=1,
+    def __init__(self, stream=None, descriptions=True, verbosity=1,
                  failfast=False, buffer=False, resultclass=None, warnings=None):
+        if stream is None:
+            stream = sys.stderr
         self.stream = _WritelnDecorator(stream)
         self.descriptions = descriptions
         self.verbosity = verbosity
diff --git a/Lib/unittest/test/test_runner.py b/Lib/unittest/test/test_runner.py
index 8f98a02..8e95410 100644
--- a/Lib/unittest/test/test_runner.py
+++ b/Lib/unittest/test/test_runner.py
@@ -299,3 +299,20 @@
             self.assertEqual(out.count(msg), 3)
         for msg in [ae_msg, at_msg]:
             self.assertEqual(out.count(msg), 1)
+
+    def testStdErrLookedUpAtInstantiationTime(self):
+        # see issue 10786
+        old_stderr = sys.stderr
+        f = io.StringIO()
+        sys.stderr = f
+        try:
+            runner = unittest.TextTestRunner()
+            self.assertTrue(runner.stream.stream is f)
+        finally:
+            sys.stderr = old_stderr
+
+    def testSpecifiedStreamUsed(self):
+        # see issue 10786
+        f = io.StringIO()
+        runner = unittest.TextTestRunner(f)
+        self.assertTrue(runner.stream.stream is f)