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Low sidelobe aperture distributions are investigated for both blocked and unblocked circular apertures. Both peak sidelobe levels and wide-angle sidelobe levels are considered. For unblocked apertures, Taylor's circular aperture synthesis technique is generalized to provide control over the wide angle sidelobe decay rate. These distributions are compared to a wide variety of alternative distributions in terms of the beamwidth, aperture efficiency, and radiated power distributions achieved for a given peak sidelobe level. A comparison is also made between the sidelobe envelopes achieved by four different distributions with a fixed beamwidth. For centrally blocked apertures, it is shown that wide angle sidelobes can be reduced by employing aperture distributions with a hole in the blocked central area.