diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 67eea980c47..7362bacbfb1 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -143,8 +143,8 @@ class BasicSocketTests(unittest.TestCase):
     def test_str_for_enums(self):
         # Make sure that the PROTOCOL_* constants have enum-like string
         # reprs.
-        proto = ssl.PROTOCOL_SSLv3
-        self.assertEqual(str(proto), '_SSLMethod.PROTOCOL_SSLv3')
+        proto = ssl.PROTOCOL_SSLv23
+        self.assertEqual(str(proto), '_SSLMethod.PROTOCOL_SSLv23')
         ctx = ssl.SSLContext(proto)
         self.assertIs(ctx.protocol, proto)
 
@@ -2384,7 +2384,8 @@ else:
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv2, True, ssl.CERT_OPTIONAL)
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv2, True, ssl.CERT_REQUIRED)
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, False)
-            try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv3, False)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_TLSv1, False)
             # SSLv23 client with specific SSL options
             if no_sslv2_implies_sslv3_hello():