diff --git a/Lib/test/test_smtplib.py b/Lib/test/test_smtplib.py
index bea3592b744..3219f725223 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -158,32 +158,6 @@ def test_debuglevel_2(self):
                               re.MULTILINE)
         self.assertRegex(stderr.getvalue(), expected)
 
-    def test_host_port_host(self):
-        mock_socket.reply_with(b"220 Hello world")
-        # create instance without arguments
-        smtp = smtplib.SMTP(f"{HOST}:{self.port}")
-        # .connect must set ._host since it is used by .starttls
-        self.assertEqual(smtp._host, HOST)
-        smtp.close()
-
-    def test_explicit_connect(self):
-        mock_socket.reply_with(b"220 Hello world")
-        # create instance without arguments
-        smtp = smtplib.SMTP()
-        # .connect must set ._host since it is used by .starttls
-        smtp.connect(HOST, self.port)
-        self.assertEqual(smtp._host, HOST)
-        smtp.close()
-
-    def test_explicit_connect_host_port(self):
-        mock_socket.reply_with(b"220 Hello world")
-        # create instance without arguments
-        smtp = smtplib.SMTP()
-        # .connect must set ._host since it is used by .starttls
-        smtp.connect(f"{HOST}:{self.port}")
-        self.assertEqual(smtp._host, HOST)
-        smtp.close()
-
 
 class SMTPGeneralTests(GeneralTests, unittest.TestCase):
 
@@ -308,6 +282,34 @@ def testBasic(self):
         # connect
         smtp = smtplib.SMTP(HOST, self.port, local_hostname='localhost',
                             timeout=support.LOOPBACK_TIMEOUT)
+        # implicit .connect must set ._host since it is used by .starttls
+        self.assertEqual(smtp._host, HOST)
+        smtp.quit()
+
+    def test_host_port_host(self):
+        # create instance with host:port notation
+        smtp = smtplib.SMTP(f"{HOST}:{self.port}", local_hostname='localhost',
+                            timeout=support.LOOPBACK_TIMEOUT)
+        # implicit .connect must set ._host since it is used by .starttls
+        self.assertEqual(smtp._host, HOST)
+        smtp.quit()
+
+    def test_explicit_connect(self):
+        # create instance without arguments
+        smtp = smtplib.SMTP(local_hostname='localhost',
+                            timeout=support.LOOPBACK_TIMEOUT)
+        # explicit .connect must set ._host since it is used by .starttls
+        smtp.connect(HOST, self.port)
+        self.assertEqual(smtp._host, HOST)
+        smtp.quit()
+
+    def test_explicit_connect_host_port(self):
+        # create instance without arguments
+        smtp = smtplib.SMTP(local_hostname='localhost',
+                            timeout=support.LOOPBACK_TIMEOUT)
+        # explicit .connect with host:port notation must set ._host, too
+        smtp.connect(f"{HOST}:{self.port}")
+        self.assertEqual(smtp._host, HOST)
         smtp.quit()
 
     def testSourceAddress(self):
diff --git a/Lib/test/test_smtpnet.py b/Lib/test/test_smtpnet.py
index e29385f4f60..86c19fa38c7 100644
--- a/Lib/test/test_smtpnet.py
+++ b/Lib/test/test_smtpnet.py
@@ -42,7 +42,7 @@ def test_connect_starttls(self):
             server.ehlo()
             server.quit()
 
-    def test_connect2_starttls(self):
+    def test_connect_host_port_starttls(self):
         support.get_attribute(smtplib, 'SMTP_SSL')
         context = ssl.SSLContext(ssl.PROTOCOL_TLS_CLIENT)
         context.check_hostname = False
@@ -59,7 +59,7 @@ def test_connect2_starttls(self):
             server.ehlo()
             server.quit()
 
-    def test_connect3_starttls(self):
+    def test_explicit_connect_starttls(self):
         support.get_attribute(smtplib, 'SMTP_SSL')
         context = ssl.SSLContext(ssl.PROTOCOL_TLS_CLIENT)
         context.check_hostname = False
@@ -77,7 +77,7 @@ def test_connect3_starttls(self):
             server.ehlo()
             server.quit()
 
-    def test_connect4_starttls(self):
+    def test_explicit_connect_host_port_starttls(self):
         support.get_attribute(smtplib, 'SMTP_SSL')
         context = ssl.SSLContext(ssl.PROTOCOL_TLS_CLIENT)
         context.check_hostname = False