ok, that saves me the work!
We also keep a separate garbage container for paper towels, use kleenex, etc. When I start a new section or redo an old one I spread that out on the ground before I lay the cardboard. Extra organic matter never hurts.
I turned a gravel parking lot into a garden plot over the course of 5 or 6 years doing this. 3 years in to the transformation I was picking 5gal buckets of tomatoes from it.