Selecting 1 From Each Group

I have a SQLite table representing a music library called songs

it looks something like this (there are many more columns, I am simplifying)

 title  |  album  |  artist
 -------|---------|----------
 a song | an album| an artist

I am trying to select a list of all albums. Now, on first thought, SELECT DISTINCT album FROM songs should work. HOWEVER, this fails if, for example, 2 artists have an album with the same title. Really what I want, is to go through each artist and select 1 of each album therein.

How might I do this?