Changing Track Numbers

Imagine a CD of say 20 songs. Each song is a table row

[Title] [Artist] [TrackNo]

I need a way for the user to change the way the songs are listed by allowing them to change the track numbers. What is the smartest way to do this? I think it would be kind of trick to have a couple of <IMG> up and down arrows per each song. The user would click on either the up or down arrow to move the song accordingly. But I don't know how to go about that. Whatever variables are passed, the process would have to check to see if there is another track# +/- 1 each time.

Then I thought maybe it would be easier to just list the songs with a form box next to each song where the user manually entered the desired order,then submit the form. But that also has it's share of issues like checking for existing track numbers, users who can't count,etc.