I recorded a bit more stuff last night. These are the results that I'm comfortable enough with other people hearing.

"A place called Home" is a Kim Richey song that I heard on Angel the first time. Great tune. Mp3 version: http://nickithansen.dk/music/a_place_called_home.mp3 

The next one is a Rufus Wainwright tune called Dinner at Eight, which I think is just delightful. I struggled with the chords on it for a long time, and it's been a while since I played it. I've sifted a version of it too, if you want to hear the real one. MP3 version: http://nickithansen.dk/music/dinner_at_eight.mp3

The last one is one of my favorite Elliott Smith tunes called Waltz #1, which is pretty damn difficult to do solo on a guitar, but I think it turned out alright. MP3 version: http://nickithansen.dk/music/waltz1.mp3