diff --git a/src/OpenSSL/SSL.py b/src/OpenSSL/SSL.py
index bdc1e4e25..8ceb2e460 100644
--- a/src/OpenSSL/SSL.py
+++ b/src/OpenSSL/SSL.py
@@ -1161,9 +1161,10 @@ def _raise_ssl_error(self, ssl, result):
                         errno = _ffi.getwinerror()[0]
                     else:
                         errno = _ffi.errno
-                    raise SysCallError(errno, errorcode.get(errno))
-                else:
-                    raise SysCallError(-1, "Unexpected EOF")
+
+                    if errno != 0:
+                        raise SysCallError(errno, errorcode.get(errno))
+                raise SysCallError(-1, "Unexpected EOF")
             else:
                 # TODO: This is untested.
                 _raise_current_error()
diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index ca28306f4..9fc5059d2 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -3557,7 +3557,7 @@ def test_shutdown(self):
         e = self.assertRaises(Error, server.recv, 1024)
         # We don't want WantReadError or ZeroReturnError or anything - it's a
         # handshake failure.
-        self.assertEquals(e.__class__, Error)
+        assert type(e) in [Error, SysCallError]
 
     def test_unexpectedEndOfFile(self):
         """