My bike has an ultegra 6700 setup with a triple crank. I thought I would need a triple living in the mountains but I don't like it anymore. I want to get a compact double ultegra. So My question is what can I get away with not replacing. I know I should technically get a new brifter, front derailleur, rear derailleur, and new chain. Could I just limit the front derailleur and shorten the chain and still have good performance from the drive train?

you don't need a new rear deraileur. I have the ultegra gs RD on my compact double and use a 12-25 casette and a 11-32 casette without issues. you also shouldn't need to shorten the chain, your long cage gs deraileur will pick up the slack. I would get the proper FD but that can be had pretty cheap and you'll probably want the appropriate brfter. i would consider tinkering with your rear casette and see if you get a better set of combos before swapping to the compact. I like my compact but don't love it, started likeing it more since I tightened up my shifting with a casette change. I like that with the triple I'm almost exclusively in the middle ring on the flats and only go to the big or the small ring when going down or up hills.

I switched from a triple to a double, what with being completely without hills, and I needed to switch the front brifter. A triple shifter will work for a double, but not well.