When two people collaborate on a song, which usually comes first, the melody or the lyrics?

I heard that when Rogers and Hammerstein created songs, Hammerstein first wrote the lyrics and then mailed them to Rogers to write the melody. This is a rather unromantic vision. I like to imagine the melody writer and the lyricist working in tandem, but this not very likely.

There are other examples of melody/lyrics collaborations, like the songs of Burt Bacharach and Hal David so beautifully rendered by Dionne Warwick, or the West Side Story songs of Leonard Bernstein and Steven Sondheim. Do the lyrics usually come first, or does it sometimes work the other way around?