Cannabis Waste Organic Bin Only Cannabis Plant Parts Belong in the Compost Leaves, flowers, and other parts from a cannabis plant can be composted as long as they do not contain or are combined with any hazardous or toxic materials. Cannabis wrapped in a cigar wrapper, cigarette rolling paper, or any other toxic materials must be disposed of in the landfill. Did You Know? History of Cannabis in the United States Other than recreational use, cannabis (fibers) can also be made into a variety of products, from rope to cloth to paper. With its usefulness, cannabis was considered a proper form of currency in Virginia, Pennsylvania and Maryland. Read more here.