Bitfinex? Honestly, I did quite a lot of trading back in the early to mid 2013, but I stopped as soon as Gox showed the first signs of insolvency (April/May 2013) and then I used Bitstamp just to cash out a bit in December 2013, but I never had any balance for more than 24 hours on it.

I'd say that there is no "super-safe" exchange for bitcoin. Not controlling directly your private keys is inherently risky. Do not have on any exchange more than you can afford to lose. Sad but true.