diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 327bb8465d7..a2b4040a9c4 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -1405,7 +1405,8 @@ else:
             try_protocol_combo(ssl.PROTOCOL_SSLv3, ssl.PROTOCOL_SSLv3, True, ssl.CERT_REQUIRED)
             if hasattr(ssl, 'PROTOCOL_SSLv2'):
                 try_protocol_combo(ssl.PROTOCOL_SSLv3, ssl.PROTOCOL_SSLv2, False)
-            try_protocol_combo(ssl.PROTOCOL_SSLv3, ssl.PROTOCOL_SSLv23, False)
+            try_protocol_combo(ssl.PROTOCOL_SSLv3, ssl.PROTOCOL_SSLv23, False,
+                               client_options=ssl.OP_NO_SSLv3)
             try_protocol_combo(ssl.PROTOCOL_SSLv3, ssl.PROTOCOL_TLSv1, False)
             if no_sslv2_implies_sslv3_hello():
                 # No SSLv2 => client will use an SSLv3 hello on recent OpenSSLs
@@ -1423,7 +1424,8 @@ else:
             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)
-            try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv23, False)
+            try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv23, False,
+                               client_options=ssl.OP_NO_TLSv1)
 
         def test_starttls(self):
             """Switching from clear text to encrypted and back again."""
diff --git a/Misc/NEWS b/Misc/NEWS
index 0b1edff6496..92f8818eb49 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -1500,6 +1500,8 @@ Extension Modules
 Tests
 -----
 
+- Issue #13218: Fix test_ssl failures on Debian/Ubuntu.
+
 - Re-enable lib2to3's test_parser.py tests, though with an expected failure
   (see issue 13125).