I edit a story at least three times. The initial edit gets rid of the typos and repetitions (sadly, there are always some!). The second edit I use to check the story makes sense in terms of its structure. The third edit is where I read the story with a reader's hat on and ask myself if the tale grips me. (It if doesn't, it won't grip anyone else!).
Everything about the story has to seem as if, of course, it belongs there. When you can't envisage taking a word out (because it will spoil the story), that's the ideal time to send your story out into the big, bad world to see if others agree with you.