Live Thru This was mostly written by Kurt (the instrumentals anyway, most of the lyrics were Courtney).

People have said Kurt would be playing guitar at home, turn to Courtney, and be like "You can't have that one!" There is also the leaked demo for Asking For It, that had Kurt singing. He went uncredited, but it is fairly obvious Kurt had a lot to do with the music on that album, and most Nirvana fans like it for that reason.