diff --git a/Lib/test/ssltests.py b/Lib/test/ssltests.py
index 9b0ed22b956..5073ae12204 100644
--- a/Lib/test/ssltests.py
+++ b/Lib/test/ssltests.py
@@ -1,17 +1,32 @@
-# Convenience test module to run all of the SSL-related tests in the
+# Convenience test module to run all of the OpenSSL-related tests in the
 # standard library.
 
+import ssl
 import sys
 import subprocess
 
-TESTS = ['test_asyncio', 'test_ftplib', 'test_hashlib', 'test_httplib',
-         'test_imaplib', 'test_nntplib', 'test_poplib', 'test_smtplib',
-         'test_smtpnet', 'test_urllib2_localnet', 'test_venv']
+TESTS = [
+    'test_asyncio', 'test_ensurepip.py', 'test_ftplib', 'test_hashlib',
+    'test_hmac', 'test_httplib', 'test_imaplib', 'test_nntplib',
+    'test_poplib', 'test_ssl', 'test_smtplib', 'test_smtpnet',
+    'test_urllib2_localnet', 'test_venv', 'test_xmlrpc'
+]
 
 def run_regrtests(*extra_args):
-    args = [sys.executable, "-m", "test"]
+    print(ssl.OPENSSL_VERSION)
+    args = [
+        sys.executable,
+        '-Werror', '-bb',  # turn warnings into exceptions
+        '-m', 'test',
+    ]
     if not extra_args:
-        args.append("-unetwork")
+        args.extend([
+            '-r',  # randomize
+            '-w',  # re-run failed tests with -v
+            '-u', 'network',  # use network
+            '-u', 'urlfetch',  # download test vectors
+            '-j', '0'  # use multiple CPUs
+        ])
     else:
         args.extend(extra_args)
     args.extend(TESTS)