An aerobic waste treatment system, such as a composting system, comprising a movable push wall (20). The movable push wall (20) is preferably part of a container (10). In use of the aerobic waste treatment system, waste is heaped against the movable push wall (20) to build a waste heap (60). The waste is coverable with a removable flexible enclosure. The removable flexible enclosure is preferably a liquid-tight but gas-permeable cover (70). A deployment apparatus (30) for covering or uncovering the waste heap (60) with the removable flexible enclosure can facilitate the handling of the removable flexible enclosure.