diff --git a/Lib/test/test_ftplib.py b/Lib/test/test_ftplib.py
index 5db70c0..aef66da 100644
--- a/Lib/test/test_ftplib.py
+++ b/Lib/test/test_ftplib.py
@@ -889,7 +889,7 @@
 
     def test_auth_ssl(self):
         try:
-            self.client.ssl_version = ssl.PROTOCOL_SSLv3
+            self.client.ssl_version = ssl.PROTOCOL_SSLv23
             self.client.auth()
             self.assertRaises(ValueError, self.client.auth)
         finally:
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 2a18cc4..67eea98 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -2410,20 +2410,24 @@
                         sys.stdout.write(
                             " SSL2 client to SSL23 server test unexpectedly failed:\n %s\n"
                             % str(x))
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, 'SSLv3')
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, 'SSLv3')
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_TLSv1, 'TLSv1')
 
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, 'SSLv3', ssl.CERT_OPTIONAL)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, 'SSLv3', ssl.CERT_OPTIONAL)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True, ssl.CERT_OPTIONAL)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_TLSv1, 'TLSv1', ssl.CERT_OPTIONAL)
 
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, 'SSLv3', ssl.CERT_REQUIRED)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, 'SSLv3', ssl.CERT_REQUIRED)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True, ssl.CERT_REQUIRED)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_TLSv1, 'TLSv1', ssl.CERT_REQUIRED)
 
             # Server with specific SSL options
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, False,
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, False,
                                server_options=ssl.OP_NO_SSLv3)
             # Will choose TLSv1
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True,
@@ -2433,6 +2437,8 @@
 
 
         @skip_if_broken_ubuntu_ssl
+        @unittest.skipUnless(hasattr(ssl, 'PROTOCOL_SSLv3'),
+                             "OpenSSL is compiled without SSLv3 support")
         def test_protocol_sslv3(self):
             """Connecting to an SSLv3 server with various client options"""
             if support.verbose:
@@ -2460,7 +2466,8 @@
             try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_TLSv1, 'TLSv1', ssl.CERT_REQUIRED)
             if hasattr(ssl, 'PROTOCOL_SSLv2'):
                 try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv2, False)
-            try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv3, False)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_TLSv1)
 
@@ -2475,7 +2482,8 @@
             try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_TLSv1_1, 'TLSv1.1')
             if hasattr(ssl, 'PROTOCOL_SSLv2'):
                 try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv2, False)
-            try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv3, False)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_TLSv1_1)
 
@@ -2497,7 +2505,8 @@
                                client_options=ssl.OP_NO_SSLv3|ssl.OP_NO_SSLv2,)
             if hasattr(ssl, 'PROTOCOL_SSLv2'):
                 try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv2, False)
-            try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv3, False)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_TLSv1_2)