The "Half-Tuck" is probably the least common way to tuck in a shirt and the hardest to pull off, however I personally love to do this with my button-down shirts. It's an easy way to make your look more casual, but still balance out your proportions by not hiding your waist-line. I recommend wearing a belt when you do this tuck to make your outfit a little more put-together. 

Also, when doing this style always remember to pul the tucked side out slightly--you don't want the shirt tight against your stomach, because it will look less proportionate with the untucked side. For the same reason, choose a shirt that isn't too long, or if it is, go with a lower waisted pant.

Next time you're feeling ambitious with your outfit, definitely try styling your button-down this way!