diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py

index d203cdd..c128dae 100644

--- a/Lib/test/test_ssl.py

+++ b/Lib/test/test_ssl.py

@@ -3256,8 +3256,9 @@ if _have_threads:

                 except ssl.SSLError as e:

                     stats = e

-                if expected is None and IS_OPENSSL_1_1:

-                    # OpenSSL 1.1.0 raises handshake error

+                if (expected is None and IS_OPENSSL_1_1

+                        and ssl.OPENSSL_VERSION_INFO < (1, 1, 0, 6)):

+                    # OpenSSL 1.1.0 to 1.1.0e raises handshake error

                     self.assertIsInstance(stats, ssl.SSLError)

                 else:

                     msg = "failed trying %s (s) and %s (c).\n" \