How do I play directly from my library?

I just downloaded Songbird 1.2.0 and added all my songs from My Music.

I have selected Shuffle and Repeat All (and have tried also with Repeat None). What I had hoped to do was use Songbird as I use iTunes: shuffling through my library directly rather than playing from playlists. I can't seem to do this on Songbird. When a song ends SB either stops playing or begins playing a song that has just played (I believe this means it is using 'Most Played' or 'Recently Played' as songlists).

I want to double-click on a song, have it play, and then have Songbird go directly to a different random song from my library of some 2,000 odd songs. Is this possible?

Thanks.