Usually, in later drafts of a story, I trim from the beginning and add to the end. Alas, I can't just shuffle words to the back of the story. (Though sometimes I can. In the story I'm working on now, I explained something too early. Fixed it with cut and paste.)
I think my first beginnings are wordy because I'm figuring out the story, and my first endings are rushed because I'm dashing for an ending. By the second draft, I have a better idea what the ending needs and the beginning can do without.