KJo on button to ultra tight player in BB shoving over ($27)

Opp's stats were 3/3 over 36 hands so he's squeaky tight. At first I thought that this one was an easy call considering that I'm getting 2:1 pot odds on the call.

However, running the ICM on this I have to be 37% to win and against 55+, A9+ and KQ I am only 35% to win. Plus, if he's any good he'll know that I know that I'm priced in to call a lot of the time so I don't think he's shoving over with complete crap.

Thoughts?

PokerStars No-Limit Hold'em Tourney, Big Blind is t150 (6 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero (t3015)
SB (t1835)
BB (t1265)
UTG (t2555)
MP (t1690)
CO (t3140)

Preflop: Hero is Button with J, K.
3 folds, Hero raises to t400, 1 fold, BB raises to t1265, Hero calls t865.

22+,A7s+,ATo+ is where you need him - with 36 hands you can't be this exact.

If you're folding to the shove I think open shoving, min raising and folding are all better.

You don't want him to call a shove, you don't want him to call pre, so basically you're bluffing but your hand is so good you're confusing yourself.

I wouldnt have thought of this ingame but I like drmcboy's idea of minraising (assuming bb is in shove/fold mode). As played it looks like a fold, I dont think the range you set for BB could get any wider