Caroline Smith and the Goodnight Sleeps' Daytrotter session. "Closing the Doors" has been my favorite so far. Lyrics such as "holding your hand never helped me forget the truth" and "closing the doors never helped me close up the rooms" stick out and keep me pushing repeat. If you're not a fan of strange voices then she won't be your favorite...but then again, maybe you shouldn't be listening to indie rock period.
And just a shout out to Daytrotter: this site is fantastic! There are free downloads of live recording sessions of some well-known and not-so-well-known artists. It's definitely worth checking out. You will have to register with your e-mail address, but there are no gimmicks. Just an e-mail here and there. So rest assured.