If the setting for
Trades reviewed by is changed from "league votes" to "commissioner", trades can be pushed through by the commish as soon as he sees it.
If its set to "none", then all trades process immediately and players are on your roster the next day.
I don't think league vote is necessary to be honest. If we use "none", and there's ever something wrong with a trade, it can always be reversed by the commish after the fact. (If I remember correctly, in the 4 years there's never been a trade voted down anyway)
Screencap is from another league