A dual-offset reflector with a foam dielectrics cone feed and a shaped subreflector is described. The antenna is designed to receive signals from direct broadcast satellites. It combines a compact design with a relatively high efficiency and low sidelobes. The paper describes the theoretical design procedure, including the shaping of the subreflector which corrects for distortions introduced by the dielectric cone. A 12 GHz model is described which has been built and successfully tested.