The paper describes the synthesis of shaped-beam dual-reflector antenna patterns using two methods. In the first, for a prescribed far field the antenna aperture field is obtained initially and then a Geometric Optics synthesis method used to define the reflector coordinates. In the second method an optimisation procedure is employed to shape the reflectors directly, so as to generate, through Physical Optics, the desired far field. The two methods are compared for the pattern corresponding to the EUTELSAT 2 spacecraft. Close agreement is found and differences ascribed to initial constraints.