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Circularly symmetric, dual-reflector, high-gain antenna systems often require feeds placed off the system's axis because of the need for multiple feeds to use the reflector antenna. Also, the constraint requiring the hyperboloid or shaped subreflector to remain circularly symmetric is sometimes added. In a Cassegrainian system, the subreflector and feed may be rotated off-axis around the paraboloid focus and retain main reflector focusing. However, substantial spillover results in considerable noise in a high-gain/low-noise temperature system. In a shaped system, the tilt of the shaped subreflector and feed together results in substantial defocusing as well as spillover noise. If the subreflector is tilted approximately one-half the angle of the feed tilt in either the Cassegrainian or the dual-shaped reflector antenna, it is found that spillover and noise are substantially reduced with tolerable defocusing. An extensive numerical analysis of these effects was conducted to determine the characteristics of a 70-meter, dual-shaped reflector versus Cassegrainian antenna and to gain some understanding of the cause of the observed effects.