google tells me that bitgrail is a small exchange!
if you paid 0.0013BTC in fees then there is nothing you can do about it, you can complain to that exchange why they are taking that big a fee from you. or stop using it and use another exchange that takes a smaller fee for withdrawals. for example i heard that poloniex and bitstamp are taking 0.0001BTC fee!
really, if we use poloniex and bitstamp very small transaction costs, we better use poloniex and bitstamp so that we do not always harmed at the time of transaction. my friends have also used poloniex and bitstamp the result is very satisfactory, they take 0.0001 BTC when transact.
There are drawbacks too on using Poloniex as a wallet.
My first time I bought goods directly with Bitcoin almost ended as a disaster. I transferred from Poloniex. They need some time - sometimes shorter, sometimes longer - to get together more withdrawals and make one bigger transaction. The payment processor had a countdown and Polo didn't do the send in that fixed time. So my transfer was not registered.
I had to talk with customer support at seller and at payment processor, spend 1-2 more days and, with some luck, it was solved. However, all the next transactions when I bought things over internet I made directly from wallet and they went on very good.
And with today's fees like 40 satoshi/byte it's again better (and safer) to keep money in your wallet imho.