AA in the SB in a multiway pot

I seem to have difficulty playing A-A in the SB when 2 or more players have already called the Big Blind when betting gets around to me pre-flop. On the one hand, if I raise, it is extremely likely that all players will call, except maybe the BB, making a good sized pot for everyone with a draw to chase after. On the other hand, if I don't raise, I'm giving all of these guys the chance to see a cheap flop and give the BB a free look at the flop. However, the pot is smaller and provides low pot odds for drawing hands.

It seems as if whenever I raise preflop, drawing hands hit. However, when I don't raise preflop, the BB hits the flop.

Thoughts? Comments?