Couldn't it be done without a fence? I'm sure I've seen pictures of piles just laying unenclosed on the ground that are a good height. The area where I live isn't very windy, so there wouldn't be a problem with the pile being blown flat or spread out if that's what you're wondering about. I'd prefer a free-standing pile since I'd have to buy the chicken wire. Aren't materials sometimes composted just using a standard pile?
