I would've shove preflop with JT with 4bbs tbh, specially if it's a tight guy, but remember.. he might call with some weaker ace or king, just because you actually only have 4bbs and he might think you're after blinds..
JhTc 44.64% 758,962 10,938
Kh7s 55.36% 942,404 10,938
You need to get there, he doesnt.. So be careful in those kinds of situations, and like mentioned above, try not to get blinded down to that small of an amount.. It's hard in some situations, but better to take a few smaller shots when 20bbs deep, than 4bbs fold/shove mode.