I think you need to clarify a little more when you say HU. Most people will immediately assume you mean "last 2 people in a STT" when it appears you just mean a 2-person pot.
In any case, both of those situations you set up seem like a set-mining type spot. Assuming both of you are fairly deep, it's quite cheap to see a flop to hit your 3 (or whatever) and try to stack villain. Later in a tournament, especially when you're down to 5-6 handed, these small PP's can't really set mine but can be used as light 3-bet hands/steal hands.
Say, instead of early and 10/20 blinds, it's the middle of the STT with 50/100 blinds. You have 15bb, BTN has 15bb. You can shove over the 3x BTN raise as a semi-bluff. If you get looked up you'll often be in a flip against Ax, KQ and those sorts of hands. If BTN limps you can make a raise intending to do a sort of go and go. Pop it to like 5x, if BTN calls then shove virtually any flop. Most of the time BTN will just lay it down and you'll scoop the pot, in both of the above scenarios.
As the pup says though, knowing the opponent is quite crucial as well.