Drawing while heads up and all-in in 2-7 TD

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Although I don't usually play the $11 2-7 TD on PokerStars, opting to work on my game in the $1.10 SnGs, this is a situation I find myself in often in 2-7 TD.

Triple Draw 2-7 Lowball Limit ($100/$200) (converter)

Hero ($2010), Seat 1
BB ($850), Seat 2
UTG ($450), Seat 3
CO ($2030), Seat 5
Button ($4110), Seat 6

Button at Seat 6.
Hero posts $50. BB posts $100.

Hand: [9h 5c 3d 7c Kd]

Round 1: (1.50 SB)

<font color="red">UTG raises. </font><font color="#666666">CO folds. </font><font color="#666666">Button folds. </font><font color="red">Hero raises. </font><font color="#666666">BB folds. </font><font color="red">UTG raises. </font><font color="green">Hero calls. </font>
Hero discards 9h Kd. UTG takes 1.

Hand: [5c 3d 7c 9d 4h]

Round 2: (9.00 SB)

<font color="red">Hero bets. </font><font color="green">UTG calls (all-in). </font>

From here on out, UTG is getting free shots to outdraw me, which begs the question: Just how strong does my hand have to be to go pat with it? In the example above, the Hero has 97, and breaking the 9 to go for a 7 is risky as a 6 will straighten him out.

So, do you pat here, and make your opponent beat your hand in two draws, or draw X number of cards here thinking your hand probably won't stand up? How does this change if the you were the player all-in?

Edit: It should have occurred to me, but it's late and I'm tired. That another important factor is the all-in player has position on me. He's all-in, so betting is taken out of the equation. However, I won't know how many he's drawing until I've made my draw. (I don't know if this makes sense, but it occurred to me that snowing by UTG is possible in this scenario, perhaps to make the Hero break a better, but vulnerable pat hand. Not sure if it will be relevant to this example, but I thought I'd float the idea out there from my stream of consciousness.) [img]/images/graemlins/smile.gif[/img]