diff --git a/kafka/conn.py b/kafka/conn.py
index 1f3bc2006..80f17009c 100644
--- a/kafka/conn.py
+++ b/kafka/conn.py
@@ -510,7 +510,7 @@ def _try_handshake(self):
         # old ssl in python2.6 will swallow all SSLErrors here...
         except (SSLWantReadError, SSLWantWriteError):
             pass
-        except (SSLZeroReturnError, ConnectionError, TimeoutError, SSLEOFError):
+        except (SSLZeroReturnError, ConnectionError, TimeoutError, SSLEOFError, ssl.SSLError, OSError) as e:
             log.warning('SSL connection closed by server during handshake.')
             self.close(Errors.KafkaConnectionError('SSL connection closed by server during handshake'))
         # Other SSLErrors will be raised to user