In Twilight what song is playing when Edward is playing the piano?

I am curious to know if anyone knows the song title and composer for the song playing when Edward is playing the piano in the movie Twilight.

I appreciate your help, thanks!

It’s called Bella’s Lullaby by Carter Burwell. I love that song. but I like the piano version better than the orchestra version.

You can listen to the only piano version here:

http://hk.youtube.com/watch?v=Ylf-Y7POLvI

Orchestra version:

http://hk.youtube.com/watch?v=gi13I1MMrT4