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A technique for generating low sidelobes on one side of the main lobe for a parabolic reflector antenna is presented. The reflector system that generates such an asymmetric sidelobe pattern consists of a central parabola with two sections of offset parabolas situated at the top and bottom of the central parabola. By adjusting the positions and dimensions of the side reflectors, considerable suppression of the first few sidelobes can be obtained. Further, by similar adjustments it is possible to achieve suppression of sidelobes on both sides of the main beam, though this suppression is relatively less. The technique, though explained in detail with reference to a cylindrical geometry, is extended for a paraboloid of revolution. The analysis program utilized for the optimization of the side reflectors is based on physical optics current integration.