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One of the basic problems of realising an optimum contoured beam, together with sidelobe suppression, is the determination of the excitation coefficients for the individual horns of a reflector and horn-array geometry. The Fletcher-Powell and the Minimax methods of optimising an arbitrary coverage with sidelobe suppression have been studied. The paper presents the formulations applicable to the Fletcher-Powell and the Minimax methods. The Brasilsat antenna is used as the test case. Results obtained using the two methods, and also by manual optimisation, are presented and compared.