diff --git a/Lib/test/test_smtplib.py b/Lib/test/test_smtplib.py
index 7991174..495764f 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -1074,6 +1074,19 @@
         self.assertRaises(UnicodeEncodeError, smtp.sendmail, 'Alice', 'Böb', '')
         self.assertRaises(UnicodeEncodeError, smtp.mail, 'Älice')
 
+    def test_send_message_error_on_non_ascii_addrs_if_no_smtputf8(self):
+        # This test is located here and not in the SMTPUTF8SimTests
+        # class because it needs a "regular" SMTP server to work
+        msg = EmailMessage()
+        msg['From'] = "Páolo <főo@bar.com>"
+        msg['To'] = 'Dinsdale'
+        msg['Subject'] = 'Nudge nudge, wink, wink \u1F609'
+        smtp = smtplib.SMTP(
+            HOST, self.port, local_hostname='localhost', timeout=3)
+        self.addCleanup(smtp.close)
+        with self.assertRaises(smtplib.SMTPNotSupportedError):
+            smtp.send_message(msg)
+
     def test_name_field_not_included_in_envelop_addresses(self):
         smtp = smtplib.SMTP(
             HOST, self.port, local_hostname='localhost', timeout=3
@@ -1218,17 +1231,6 @@
         self.assertIn('SMTPUTF8', self.serv.last_mail_options)
         self.assertEqual(self.serv.last_rcpt_options, [])
 
-    def test_send_message_error_on_non_ascii_addrs_if_no_smtputf8(self):
-        msg = EmailMessage()
-        msg['From'] = "Páolo <főo@bar.com>"
-        msg['To'] = 'Dinsdale'
-        msg['Subject'] = 'Nudge nudge, wink, wink \u1F609'
-        smtp = smtplib.SMTP(
-            HOST, self.port, local_hostname='localhost', timeout=3)
-        self.addCleanup(smtp.close)
-        self.assertRaises(smtplib.SMTPNotSupportedError,
-                          smtp.send_message(msg))
-
 
 EXPECTED_RESPONSE = encode_base64(b'\0psu\0doesnotexist', eol='')
 
@@ -1296,18 +1298,5 @@
         self.assertEqual(code, 235)
 
 
-@support.reap_threads
-def test_main(verbose=None):
-    support.run_unittest(
-        BadHELOServerTests,
-        DebuggingServerTests,
-        GeneralTests,
-        NonConnectingTests,
-        SMTPAUTHInitialResponseSimTests,
-        SMTPSimTests,
-        TooLongLineTests,
-        )
-
-
 if __name__ == '__main__':
-    test_main()
+    unittest.main()
diff --git a/Misc/NEWS.d/next/Tests/2018-01-25-18-10-47.bpo-32663.IKDsqu.rst b/Misc/NEWS.d/next/Tests/2018-01-25-18-10-47.bpo-32663.IKDsqu.rst
new file mode 100644
index 0000000..8357284
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2018-01-25-18-10-47.bpo-32663.IKDsqu.rst
@@ -0,0 +1,2 @@
+Making sure the `SMTPUTF8SimTests` class of tests gets run in
+test_smtplib.py.