diff --git a/.travis.yml b/.travis.yml
index ab43318..3a5d203 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -12,7 +12,7 @@
 
 env:
   global:
-    - OPENSSL=1.1.0g
+    - OPENSSL=1.1.0h
     - OPENSSL_DIR="$HOME/multissl/openssl/${OPENSSL}"
     - PATH="${OPENSSL_DIR}/bin:$PATH"
     # Use -O3 because we don't use debugger on Travis-CI
diff --git a/Doc/library/ssl.rst b/Doc/library/ssl.rst
index dcb2666..2ccea13 100644
--- a/Doc/library/ssl.rst
+++ b/Doc/library/ssl.rst
@@ -169,11 +169,6 @@
 
      3DES was dropped from the default cipher string.
 
-   .. versionchanged:: 3.7
-
-     TLS 1.3 cipher suites TLS_AES_128_GCM_SHA256, TLS_AES_256_GCM_SHA384,
-     and TLS_CHACHA20_POLY1305_SHA256 were added to the default cipher string.
-
 
 Exceptions
 ^^^^^^^^^^
@@ -1601,6 +1596,9 @@
       when connected, the :meth:`SSLSocket.cipher` method of SSL sockets will
       give the currently selected cipher.
 
+      OpenSSL 1.1.1 has TLS 1.3 cipher suites enabled by default. The suites
+      cannot be disabled with :meth:`~SSLContext.set_ciphers`.
+
 .. method:: SSLContext.set_alpn_protocols(protocols)
 
    Specify which protocols the socket should advertise during the SSL/TLS
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 36580d5..9017ad5 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -2716,10 +2716,7 @@
     def test_ecc_cert(self):
         client_context = ssl.SSLContext(ssl.PROTOCOL_TLS_CLIENT)
         client_context.load_verify_locations(SIGNING_CA)
-        client_context.set_ciphers(
-            'TLS13-AES-128-GCM-SHA256:TLS13-CHACHA20-POLY1305-SHA256:'
-            'ECDHE:ECDSA:!NULL:!aRSA'
-        )
+        client_context.set_ciphers('ECDHE:ECDSA:!NULL:!aRSA')
         hostname = SIGNED_CERTFILE_ECC_HOSTNAME
 
         server_context = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
@@ -3466,17 +3463,16 @@
                 sock.do_handshake()
             self.assertEqual(cm.exception.errno, errno.ENOTCONN)
 
-    def test_default_ciphers(self):
-        context = ssl.SSLContext(ssl.PROTOCOL_TLS)
-        try:
-            # Force a set of weak ciphers on our client context
-            context.set_ciphers("DES")
-        except ssl.SSLError:
-            self.skipTest("no DES cipher available")
-        with ThreadedEchoServer(CERTFILE,
-                                ssl_version=ssl.PROTOCOL_TLS,
-                                chatty=False) as server:
-            with context.wrap_socket(socket.socket()) as s:
+    def test_no_shared_ciphers(self):
+        client_context, server_context, hostname = testing_context()
+        # OpenSSL enables all TLS 1.3 ciphers, enforce TLS 1.2 for test
+        client_context.options |= ssl.OP_NO_TLSv1_3
+        # Force different suites on client and master
+        client_context.set_ciphers("AES128")
+        server_context.set_ciphers("AES256")
+        with ThreadedEchoServer(context=server_context) as server:
+            with client_context.wrap_socket(socket.socket(),
+                                            server_hostname=hostname) as s:
                 with self.assertRaises(OSError):
                     s.connect((HOST, server.port))
         self.assertIn("no shared cipher", server.conn_errors[0])
@@ -3517,9 +3513,9 @@
             with context.wrap_socket(socket.socket()) as s:
                 s.connect((HOST, server.port))
                 self.assertIn(s.cipher()[0], {
-                    'TLS13-AES-256-GCM-SHA384',
-                    'TLS13-CHACHA20-POLY1305-SHA256',
-                    'TLS13-AES-128-GCM-SHA256',
+                    'TLS_AES_256_GCM_SHA384',
+                    'TLS_CHACHA20_POLY1305_SHA256',
+                    'TLS_AES_128_GCM_SHA256',
                 })
                 self.assertEqual(s.version(), 'TLSv1.3')
 
@@ -3925,23 +3921,20 @@
 
     def test_shared_ciphers(self):
         client_context, server_context, hostname = testing_context()
-        if ssl.OPENSSL_VERSION_INFO >= (1, 0, 2):
-            client_context.set_ciphers("AES128:AES256")
-            server_context.set_ciphers("AES256")
-            alg1 = "AES256"
-            alg2 = "AES-256"
-        else:
-            client_context.set_ciphers("AES:3DES")
-            server_context.set_ciphers("3DES")
-            alg1 = "3DES"
-            alg2 = "DES-CBC3"
+        client_context.set_ciphers("AES128:AES256")
+        server_context.set_ciphers("AES256")
+        expected_algs = [
+            "AES256", "AES-256",
+            # TLS 1.3 ciphers are always enabled
+            "TLS_CHACHA20", "TLS_AES",
+        ]
 
         stats = server_params_test(client_context, server_context,
                                    sni_name=hostname)
         ciphers = stats['server_shared_ciphers'][0]
         self.assertGreater(len(ciphers), 0)
         for name, tls_version, bits in ciphers:
-            if not alg1 in name.split("-") and alg2 not in name:
+            if not any(alg in name for alg in expected_algs):
                 self.fail(name)
 
     def test_read_write_after_close_raises_valuerror(self):
diff --git a/Misc/NEWS.d/next/Library/2018-05-18-21-50-47.bpo-33570.7CZy4t.rst b/Misc/NEWS.d/next/Library/2018-05-18-21-50-47.bpo-33570.7CZy4t.rst
new file mode 100644
index 0000000..bd719a4
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2018-05-18-21-50-47.bpo-33570.7CZy4t.rst
@@ -0,0 +1,3 @@
+Change TLS 1.3 cipher suite settings for compatibility with OpenSSL
+1.1.1-pre6 and newer. OpenSSL 1.1.1 will have TLS 1.3 cipers enabled by
+default.
diff --git a/Tools/ssl/multissltests.py b/Tools/ssl/multissltests.py
index 2efc425..bbc5c66 100755
--- a/Tools/ssl/multissltests.py
+++ b/Tools/ssl/multissltests.py
@@ -45,16 +45,16 @@
 ]
 
 OPENSSL_RECENT_VERSIONS = [
-    "1.0.2n",
-    "1.1.0g",
-    "1.1.1-pre1",
+    "1.0.2o",
+    "1.1.0h",
+    "1.1.1-pre6",
 ]
 
 LIBRESSL_OLD_VERSIONS = [
 ]
 
 LIBRESSL_RECENT_VERSIONS = [
-    "2.7.1",
+    "2.7.3",
 ]
 
 # store files in ../multissl