Which one is for you? 0.0000691 BTC or 1.2048 BTC? If it's the first one, it's less than the fee so you can't really use it for anything. If it's the other, I don't really get why the sender kept that small change. It could just as well be added to the fee.
In your case with 373 0.003 btc should be enough.
You missed a zero there: 0.0003
BTC should be enough for very fast confirmation.