How can I remove a song from options for creating an alarm?

iOS 6 added the ability to use a song from your music library as the "Sound" for an alarm. Whenever you use a song - it stays in the list of songs to select in the future. Is there anyway to clear this list or remove a song from the list?


You can’t clear this list or remove a song, unfortunately, but the list is limited to 5 songs, so adding new songs will clear previous ones.

I noticed this so I said, dammit, I might as well set one song for each workday. :)