A new description of the profiles of the main reflector and subreflector of a dual-reflector antenna is given in terms of a single parameter, the angle subtended by the normal to the main reflector and the axis of the system. It is shown that the same parameter describes the nature of the focusing in both the illuminating beam and the image space. Hence, quite general illumination, focusing and main reflector profiles can be considered. The results are illustrated for subreflectors in the concave hemisphere and paraboloid, for axial illumination and offset conditions, and the application of the method to amplitude shaping or the Abbe sine condition is discussed.