There is provided an apparatus for composting organic waste in a container with an uneven aeration floor positioned above the bottom of the container. Preferably, the aeration floor slopes down and in from its outer edges to encourage liquid formed during composting to collect under the perforated center portion of the aeration floor. Preferably, the perforated center portion of the aeration floor is arched or peaked. This particular aeration floor configuration directs more air toward the center of the composting mass while minimizing the amount of air following the path of least resistance up the side wall. A chamber is defined by the aeration floor and the bottom of the container. Air enters (or exits) the chamber through an orifice and exits (or enters) the chamber through the perforations in the aeration floor. The container may also have a top wall or cover and a means for exhausting or introducing air through the top of the container. A reversing damper may be used simplify controlling air flow direction. Preferably, the apparatus can be modified to also dewater liquid organic waste before composting.