I'm the other type. Still "have to be in my inspired mood" but: I go back and rewrite as I'm writing. I can't stand leaving mistakes on the page. I also delete and redo when I have a better idea, or realize a different word would sound better, or suddenly realize two people are actually brothers, etc.
According to Kurt Vonnegut: Tellers of stories with ink on paper, not that they matter any more, have been either swoopers or bashers. Swoopers write a story quickly, higgledy-piggledy, crinkum-crankum, any which way. Then they go over it again painstakingly, fixing everything that is just plain awful or doesn't work. Bashers go one sentence at a time, getting it exactly right before they go on to the next one. When they're done they're done.
He thinks more men are bashers and women are swoopers, but I don't know if I agree.