The Half Tuck
The half-tuck is one of those things that is easy to do, but also easy to screw up. It takes the right amount of meticulousness and carefree attitude to get it perfect. I usually leave the bottom 3 button unbuttoned, which gives you enough of one side to tuck and the other side to leave out, to give you the polished/disheveled look you're going for.
Give it a try and let me know how it works out for you!