This is a discussion on Top 10 stack with less than 150 left within the online poker forums, in the Tournament Poker section; 8 handed, blinds are 4k/8k ante 960
UTG +1 raises 3xbb (villian) (39bb)
Folds to the big blind, 3bet to 10.5 bb (hero) (89bb) with KK
I can't imagine too many things that would have saved you money. This is the advantage of having one of the big stacks. I might have called the BB, and still could have ended up all in by the river unless an ace showed.
What was your goal in raising? Was it to build the pot or to scare him off? When villain shoved, what hands could you put him on (that you beat)?
I don't think you made any errors, even if I might have played it smaller/slower.