diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 48c4fecabd14fd..a32b0bcc7e22b0 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -1106,6 +1106,7 @@ def test_hostname_checks_common_name(self):
 
     @unittest.skipUnless(hasattr(ssl.SSLContext, 'minimum_version'),
                          "required OpenSSL 1.1.0g")
+    @unittest.skipIf(IS_LIBRESSL, "see bpo-34001")
     def test_min_max_version(self):
         ctx = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
         # OpenSSL default is MINIMUM_SUPPORTED, however some vendors like
@@ -3726,8 +3727,8 @@ def test_min_max_version(self):
                 self.assertEqual(s.version(), 'TLSv1.1')
 
         # client 1.0, server 1.2 (mismatch)
-        server_context.minimum_version = ssl.TLSVersion.TLSv1_2
         server_context.maximum_version = ssl.TLSVersion.TLSv1_2
+        server_context.minimum_version = ssl.TLSVersion.TLSv1_2
         client_context.maximum_version = ssl.TLSVersion.TLSv1
         client_context.maximum_version = ssl.TLSVersion.TLSv1
         with ThreadedEchoServer(context=server_context) as server:
diff --git a/Misc/NEWS.d/next/Tests/2019-06-03-20-47-10.bpo-34001.KvYx9z.rst b/Misc/NEWS.d/next/Tests/2019-06-03-20-47-10.bpo-34001.KvYx9z.rst
new file mode 100644
index 00000000000000..35c65a8fbf0fa4
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-06-03-20-47-10.bpo-34001.KvYx9z.rst
@@ -0,0 +1,2 @@
+Make test_ssl pass with LibreSSL. LibreSSL handles minimum and maximum TLS
+version differently than OpenSSL.