diff --git a/Lib/enum.py b/Lib/enum.py
index e79b038..056400d 100644
--- a/Lib/enum.py
+++ b/Lib/enum.py
@@ -690,7 +690,9 @@
             pseudo_member = object.__new__(cls)
             pseudo_member._name_ = None
             pseudo_member._value_ = value
-            cls._value2member_map_[value] = pseudo_member
+            # use setdefault in case another thread already created a composite
+            # with this value
+            pseudo_member = cls._value2member_map_.setdefault(value, pseudo_member)
         return pseudo_member
 
     def __contains__(self, other):
@@ -785,7 +787,9 @@
                 pseudo_member = int.__new__(cls, value)
                 pseudo_member._name_ = None
                 pseudo_member._value_ = value
-                cls._value2member_map_[value] = pseudo_member
+                # use setdefault in case another thread already created a composite
+                # with this value
+                pseudo_member = cls._value2member_map_.setdefault(value, pseudo_member)
         return pseudo_member
 
     def __or__(self, other):
@@ -835,18 +839,21 @@
     # _decompose is only called if the value is not named
     not_covered = value
     negative = value < 0
+    # issue29167: wrap accesses to _value2member_map_ in a list to avoid race
+    #             conditions between iterating over it and having more psuedo-
+    #             members added to it
     if negative:
         # only check for named flags
         flags_to_check = [
                 (m, v)
-                for v, m in flag._value2member_map_.items()
+                for v, m in list(flag._value2member_map_.items())
                 if m.name is not None
                 ]
     else:
         # check for named flags and powers-of-two flags
         flags_to_check = [
                 (m, v)
-                for v, m in flag._value2member_map_.items()
+                for v, m in list(flag._value2member_map_.items())
                 if m.name is not None or _power_of_two(v)
                 ]
     members = []
diff --git a/Lib/test/test_enum.py b/Lib/test/test_enum.py
index e97ef94..13a89fc 100644
--- a/Lib/test/test_enum.py
+++ b/Lib/test/test_enum.py
@@ -7,6 +7,11 @@
 from io import StringIO
 from pickle import dumps, loads, PicklingError, HIGHEST_PROTOCOL
 from test import support
+try:
+    import threading
+except ImportError:
+    threading = None
+
 
 # for pickle tests
 try:
@@ -1983,6 +1988,45 @@
             d = 6
         self.assertEqual(repr(Bizarre(7)), '<Bizarre.d|c|b: 7>')
 
+    @unittest.skipUnless(threading, 'Threading required for this test.')
+    @support.reap_threads
+    def test_unique_composite(self):
+        # override __eq__ to be identity only
+        class TestFlag(Flag):
+            one = auto()
+            two = auto()
+            three = auto()
+            four = auto()
+            five = auto()
+            six = auto()
+            seven = auto()
+            eight = auto()
+            def __eq__(self, other):
+                return self is other
+            def __hash__(self):
+                return hash(self._value_)
+        # have multiple threads competing to complete the composite members
+        seen = set()
+        failed = False
+        def cycle_enum():
+            nonlocal failed
+            try:
+                for i in range(256):
+                    seen.add(TestFlag(i))
+            except Exception:
+                failed = True
+        threads = [
+                threading.Thread(target=cycle_enum)
+                for _ in range(8)
+                ]
+        with support.start_threads(threads):
+            pass
+        # check that only 248 members were created
+        self.assertFalse(
+                failed,
+                'at least one thread failed while creating composite members')
+        self.assertEqual(256, len(seen), 'too many composite members created')
+
 
 class TestIntFlag(unittest.TestCase):
     """Tests of the IntFlags."""
@@ -2275,6 +2319,46 @@
         for f in Open:
             self.assertEqual(bool(f.value), bool(f))
 
+    @unittest.skipUnless(threading, 'Threading required for this test.')
+    @support.reap_threads
+    def test_unique_composite(self):
+        # override __eq__ to be identity only
+        class TestFlag(IntFlag):
+            one = auto()
+            two = auto()
+            three = auto()
+            four = auto()
+            five = auto()
+            six = auto()
+            seven = auto()
+            eight = auto()
+            def __eq__(self, other):
+                return self is other
+            def __hash__(self):
+                return hash(self._value_)
+        # have multiple threads competing to complete the composite members
+        seen = set()
+        failed = False
+        def cycle_enum():
+            nonlocal failed
+            try:
+                for i in range(256):
+                    seen.add(TestFlag(i))
+            except Exception:
+                failed = True
+        threads = [
+                threading.Thread(target=cycle_enum)
+                for _ in range(8)
+                ]
+        with support.start_threads(threads):
+            pass
+        # check that only 248 members were created
+        self.assertFalse(
+                failed,
+                'at least one thread failed while creating composite members')
+        self.assertEqual(256, len(seen), 'too many composite members created')
+
+
 class TestUnique(unittest.TestCase):
 
     def test_unique_clean(self):
@@ -2484,7 +2568,8 @@
 class TestIntEnumConvert(unittest.TestCase):
     def test_convert_value_lookup_priority(self):
         test_type = enum.IntEnum._convert(
-                'UnittestConvert', 'test.test_enum',
+                'UnittestConvert',
+                ('test.test_enum', '__main__')[__name__=='__main__'],
                 filter=lambda x: x.startswith('CONVERT_TEST_'))
         # We don't want the reverse lookup value to vary when there are
         # multiple possible names for a given value.  It should always
@@ -2493,7 +2578,8 @@
 
     def test_convert(self):
         test_type = enum.IntEnum._convert(
-                'UnittestConvert', 'test.test_enum',
+                'UnittestConvert',
+                ('test.test_enum', '__main__')[__name__=='__main__'],
                 filter=lambda x: x.startswith('CONVERT_TEST_'))
         # Ensure that test_type has all of the desired names and values.
         self.assertEqual(test_type.CONVERT_TEST_NAME_F,