What kind of strings should I put on my Tele style electric guitar to give it a nice jazz tone?

It's a G&L ASAT Special Tribute Series guitar, practically a Tele. Well all I'm playing now is jazz on it so I'm wondering what strings to use to give it a great jazz tone, not a jazz guitar at all though. I've always has about 9s on it, fine for bending but horrible for jazz. I switched to some 11s, jazziest ones my local shop had and they're better once I got used to them but still not very good. They feel too loose and weak still now I'm used to them, they're also a bit unbalanced I swear the b came from a lighter set. So what gauge should I go to? Also it felt really bad putting the heavier set on the little skinny electric, how safe is it to put on even heavier ones? Thanks.