diff --git a/tests/test_connection.py b/tests/test_connection.py
index 58c1bd7e..06463383 100644
--- a/tests/test_connection.py
+++ b/tests/test_connection.py
@@ -34,9 +34,7 @@
 import logging
 import os
 import platform
-import ssl
 import socket
-import subprocess
 import sys
 import timeit
 import unittest
@@ -2451,8 +2449,14 @@ def test_connection_attributes_defaults(self):
         "This test fails due to a bug on macOS 12",
     )
     @unittest.skipIf(tests.MYSQL_VERSION < (5, 7, 40), "TLSv1.1 incompatible")
-    @unittest.skipUnless(ssl.HAS_TLSv1, "TLSv1 not available")
-    @unittest.skipUnless(ssl.HAS_TLSv1_1, "TLSv1.1 not available")
+    @unittest.skipIf(
+        tests.MYSQL_VERSION > (8, 0, 27),
+        "TLSv1 and TLSv1.1 support removed as of MySQL 8.0.28",
+    )
+    @unittest.skipIf(
+        tests.MYSQL_VERSION > (5, 7, 36) and tests.MYSQL_VERSION < (5, 8, 0),
+        "TLSv1 and TLSv1.1 support removed as of MySQL 5.7.37",
+    )
     @tests.foreach_cnx()
     def test_get_connection_with_tls_version(self):
         if isinstance(self.cnx, connection.MySQLConnection):
diff --git a/tests/test_mysqlx_connection.py b/tests/test_mysqlx_connection.py
index 928fff25..84ddef17 100644
--- a/tests/test_mysqlx_connection.py
+++ b/tests/test_mysqlx_connection.py
@@ -35,7 +35,6 @@
 import os
 import platform
 import random
-import ssl
 import socket
 import string
 import struct
@@ -1348,8 +1347,14 @@ def test_ssl_connection(self):
         "This test fails due to a bug on macOS 12",
     )
     @unittest.skipIf(tests.MYSQL_VERSION < (5, 7, 40), "TLSv1.1 incompatible")
-    @unittest.skipUnless(ssl.HAS_TLSv1, "TLSv1 not available")
-    @unittest.skipUnless(ssl.HAS_TLSv1_1, "TLSv1.1 not available")
+    @unittest.skipIf(
+        tests.MYSQL_VERSION > (8, 0, 27),
+        "TLSv1 and TLSv1.1 support removed as of MySQL 8.0.28",
+    )
+    @unittest.skipIf(
+        tests.MYSQL_VERSION > (5, 7, 36) and tests.MYSQL_VERSION < (5, 8, 0),
+        "TLSv1 and TLSv1.1 support removed as of MySQL 5.7.37",
+    )
     def test_get_session_with_tls_version(self):
         # Test None value is returned if no schema name is specified
         settings = self.connect_kwargs.copy()