diff --git a/Lib/test/test_uuid.py b/Lib/test/test_uuid.py
index 89e221bef1b..c22b6af3e08 100644
--- a/Lib/test/test_uuid.py
+++ b/Lib/test/test_uuid.py
@@ -292,14 +292,8 @@ class TestUUID(TestCase):
         badtype(lambda: setattr(u, 'node', 0))
 
     def check_node(self, node, source):
-        individual_group_bit = (node >> 40) & 1
-        universal_local_bit = (node >> 40) & 2
-        message = "%012x doesn't look like a real MAC address" % node
-        self.assertEqual(individual_group_bit, 0, message)
-        self.assertEqual(universal_local_bit, 0, message)
-        self.assertNotEqual(node, 0, message)
-        self.assertNotEqual(node, 0xffffffffffff, message)
-        self.assertTrue(0 <= node, message)
+        message = "%012x is not an RFC 4122 node ID" % node
+        self.assertTrue(0 < node, message)
         self.assertTrue(node < (1 << 48), message)
 
         TestUUID.source2node[source] = node
@@ -318,10 +312,6 @@ class TestUUID(TestCase):
 
     def test_ifconfig_getnode(self):
         import sys
-        print("""    WARNING: uuid._ifconfig_getnode is unreliable on many platforms.
-        It is disabled until the code and/or test can be fixed properly.""", file=sys.__stdout__)
-        return
-
         import os
         if os.name == 'posix':
             node = uuid._ifconfig_getnode()
@@ -341,18 +331,18 @@ class TestUUID(TestCase):
 
     def test_random_getnode(self):
         node = uuid._random_getnode()
-        self.assertTrue(0 <= node)
-        self.assertTrue(node < (1 <<48))
+        # Least significant bit of first octet must be set.
+        self.assertTrue(node & 0x010000000000)
+        self.assertTrue(node < (1 << 48))
 
     def test_unixdll_getnode(self):
         import sys
-        print("""    WARNING: uuid._unixdll_getnode is unreliable on many platforms.
-        It is disabled until the code and/or test can be fixed properly.""", file=sys.__stdout__)
-        return
-
         import os
         if importable('ctypes') and os.name == 'posix':
-            self.check_node(uuid._unixdll_getnode(), 'unixdll')
+            try: # Issues 1481, 3581: _uuid_generate_time() might be None.
+                self.check_node(uuid._unixdll_getnode(), 'unixdll')
+            except TypeError:
+                pass
 
     def test_windll_getnode(self):
         import os
@@ -361,10 +351,6 @@ class TestUUID(TestCase):
 
     def test_getnode(self):
         import sys
-        print("""    WARNING: uuid.getnode is unreliable on many platforms.
-        It is disabled until the code and/or test can be fixed properly.""", file=sys.__stdout__)
-        return
-
         node1 = uuid.getnode()
         self.check_node(node1, "getnode1")