diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 7f6b93148f4527..cde521c123ddbb 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -1066,8 +1066,11 @@ def test_hostname_checks_common_name(self):
                          "required OpenSSL 1.1.0g")
     def test_min_max_version(self):
         ctx = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
-        self.assertEqual(
-            ctx.minimum_version, ssl.TLSVersion.MINIMUM_SUPPORTED
+        # OpenSSL default is MINIMUM_SUPPORTED, however some vendors like
+        # Fedora override the setting to TLS 1.0.
+        self.assertIn(
+            ctx.minimum_version,
+            {ssl.TLSVersion.MINIMUM_SUPPORTED, ssl.TLSVersion.TLSv1}
         )
         self.assertEqual(
             ctx.maximum_version, ssl.TLSVersion.MAXIMUM_SUPPORTED
diff --git a/Misc/NEWS.d/next/Tests/2019-01-10-18-35-42.bpo-35045.qdd6d9.rst b/Misc/NEWS.d/next/Tests/2019-01-10-18-35-42.bpo-35045.qdd6d9.rst
new file mode 100644
index 00000000000000..630a22d77868c5
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-01-10-18-35-42.bpo-35045.qdd6d9.rst
@@ -0,0 +1,2 @@
+Make ssl tests less strict and also accept TLSv1 as system default. The
+changes unbreaks test_min_max_version on Fedora 29.