It is well known that the conventional on-axis gain of an aperture-type antenna is maximized when the aperture illumination pattern has uniform amplitude and phase. For backscatter radar measurements, however, the distributed target brings the off-axis gain into play, and the sensitivity is proportional to the square of the gain averaged over the solid angle of the beam. It has been assumed that this backscatter gain, like on-axis gain, is maximized when the illumination is uniform. We show that this is not quite the case; for a fixed aperture area the backscatter gain can be increased at least 6% by using the kind of amplitude taper that reduces sidelobe levels. It is also well known that the maximum on-axis gain is proportional to the area of the aperture but independent of the shape. We show that this is not the case for backscatter gain.