Name that tune - German(?) Lullabye

If someone recognizes this melody, I would love to know the composer. My only exposure to it is from a music box, probably Swiss or German, like the ones in the intro.

Played on a Brüko mahogany baritone ukulele
Living Water custom baritone strings in Linear A tuning ( E A C# F#)

You're right, it's German. It's called "Wiegenlied" and was composed by Johannes Brahms.

You had me excited for a minute as I didn't recognize that title, but no, it is not Wiegenlied, unless there is more than one tune by that name. Here is the most famous one and it is clearly a completely different melody - http://www.youtube.com/watch?v=EBIKYRXGz2k