Good hand vs. short stack...build side pot or trap dead money?

[tipperdog]

Played this hand last night, but am more interested in thoughts on the general principal, namely, what to do when you have a good but not great hand and face a raise from a short stack and call from a big stack before you act. You reasonably think that you're ahead of both hands. Do you raise to isolate against the shortie and add some dead money to the pot or try to build a side pot?

Here's the hand in question, but again, I'd welcome thoughts on the situation generally.

Playing 1/2 NL on FullTilt.

MP has $21 and just lost a huge pot. I believe he is titly and will call any raise I make. His range of hands here is very large and rates to be worse than my QQ. OTB has $200 and seems to be a typical player. I highly doubt that his flat call is a fancy trap. It's more likely that he has a pair or some kind speculative suited hand. I have $250 in the BB.

MP open-raises to $7. OTB calls. I pick up QQ in the BB. I raise to $31, MP calls all-in and OTB folds. MP shows A9s and my hand holds up.

[Iconoclastic]

Standard. Many times I get the overlay and in my entire poker playing career only once did the cold caller have something that beat me (Aces). It's better to take out the caller. You don't want a Ace or King to come on the flop, which happens about 40% of the time.