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Exchange bias effects have been studied in elliptical dots composed of ferromagnetic Ni80Fe20-antiferromagnetic Ir20Mn80 bilayers. The magnetization reversal mechanisms and magnetic configurations have been investigated by magneto-optic Kerr effect and magnetic force microscopy. Although the obtained bias fields in these dots are relatively small, the magnetization reversal is found to be influenced by the ferromagnetic-antiferromagnetic coupling. Namely, for some off-axis angles of measurement, the magnetization reversal mechanism of the Ni80Fe20-Ir20Mn80 ellipses depends on whether exchange bias is induced along the minor or major axis of the ellipses. Hence, exchange bias is shown to be an effective means for tailoring the magnetization reversal of elliptical dots after sample fabrication.