diff --git a/scrapy/core/downloader/tls.py b/scrapy/core/downloader/tls.py
index 2ba72593f..7e5882663 100644
--- a/scrapy/core/downloader/tls.py
+++ b/scrapy/core/downloader/tls.py
@@ -74,11 +74,18 @@ if twisted_version >= (14, 0, 0):
             if where & SSL_CB_HANDSHAKE_START:
                 set_tlsext_host_name(connection, self._hostnameBytes)
             elif where & SSL_CB_HANDSHAKE_DONE:
-                logger.debug('SSL connection to %s using protocol %s, cipher %s',
-                             self._hostnameASCII,
-                             connection.get_protocol_version_name(),
-                             connection.get_cipher_name(),
-                             )
+                if hasattr(connection, 'get_cipher_name'):  # requires pyOPenSSL 0.15
+                    if hasattr(connection, 'get_protocol_version_name'):  # requires pyOPenSSL 16.0.0
+                        logger.debug('SSL connection to %s using protocol %s, cipher %s',
+                                     self._hostnameASCII,
+                                     connection.get_protocol_version_name(),
+                                     connection.get_cipher_name(),
+                                     )
+                    else:
+                        logger.debug('SSL connection to %s using cipher %s',
+                                     self._hostnameASCII,
+                                     connection.get_cipher_name(),
+                                     )
                 server_cert = connection.get_peer_certificate()
                 logger.debug('SSL connection certificate: issuer "%s", subject "%s"',
                              x509name_to_string(server_cert.get_issuer()),