Based on https://github.com/python/cpython/pull/6210.

--- Lib/test/test_ssl.py.orig
+++ Lib/test/test_ssl.py
@@ -1687,6 +1687,7 @@ def test_get_ca_certs_capath(self):
         self.assertEqual(len(ctx.get_ca_certs()), 1)
 
     @needs_sni
+    @unittest.skipUnless(hasattr(ssl, "PROTOCOL_TLSv1_2"), "needs TLS 1.2")
     def test_context_setget(self):
         # Check that the context of a connected socket can be replaced.
         ctx1 = ssl.SSLContext(ssl.PROTOCOL_TLSv1_2)
--- Modules/_ssl.c.orig
+++ Modules/_ssl.c
@@ -106,6 +106,12 @@ struct py_ssl_library_code {
 
 #if (OPENSSL_VERSION_NUMBER >= 0x10100000L) && !defined(LIBRESSL_VERSION_NUMBER)
 #  define OPENSSL_VERSION_1_1 1
+#  define PY_OPENSSL_1_1_API 1
+#endif
+
+/* LibreSSL 2.7.0 provides necessary OpenSSL 1.1.0 APIs */
+#if defined(LIBRESSL_VERSION_NUMBER) && LIBRESSL_VERSION_NUMBER >= 0x2070000fL
+#  define PY_OPENSSL_1_1_API 1
 #endif
 
 /* Openssl comes with TLSv1.1 and TLSv1.2 between 1.0.0h and 1.0.1
@@ -152,16 +158,18 @@ struct py_ssl_library_code {
 #define INVALID_SOCKET (-1)
 #endif
 
-#ifdef OPENSSL_VERSION_1_1
-/* OpenSSL 1.1.0+ */
-#ifndef OPENSSL_NO_SSL2
-#define OPENSSL_NO_SSL2
-#endif
-#else /* OpenSSL < 1.1.0 */
-#if defined(WITH_THREAD)
+/* OpenSSL 1.0.2 and LibreSSL needs extra code for locking */
+#if !defined(OPENSSL_VERSION_1_1) && defined(WITH_THREAD)
 #define HAVE_OPENSSL_CRYPTO_LOCK
 #endif
 
+#if defined(OPENSSL_VERSION_1_1) && !defined(OPENSSL_NO_SSL2)
+#define OPENSSL_NO_SSL2
+#endif
+
+#ifndef PY_OPENSSL_1_1_API
+/* OpenSSL 1.1 API shims for OpenSSL < 1.1.0 and LibreSSL < 2.7.0 */
+
 #define TLS_method SSLv23_method
 #define TLS_client_method SSLv23_client_method
 #define TLS_server_method SSLv23_server_method
@@ -227,7 +235,7 @@ SSL_SESSION_get_ticket_lifetime_hint(const SSL_SESSION *s)
     return s->tlsext_tick_lifetime_hint;
 }
 
-#endif /* OpenSSL < 1.1.0 or LibreSSL */
+#endif /* OpenSSL < 1.1.0 or LibreSSL < 2.7.0 */
 
 
 enum py_ssl_error {
--- Tools/ssl/multissltests.py.orig
+++ Tools/ssl/multissltests.py
@@ -57,8 +57,9 @@
 ]
 
 LIBRESSL_RECENT_VERSIONS = [
-    "2.5.3",
     "2.5.5",
+    "2.6.4",
+    "2.7.1",
 ]
 
 # store files in ../multissl