It is well known that phase errors introduced during the formation of synthetic antenna apertures and in the data-processing stages of pulse-compression radars degrade system performance. Expressions are presented from which the upper bounds of the degradation effects of small arbitrary phase errors on the azimuth resolution of synthetic apertures and the range resolution of pulse-compression radars can be calculated. It is not necessary to know the exact phase-error function; only the peak phase deviation need be given or estimated. These expressions allow the use of amplitude weighting factors for sidelobe reduction, and the effect of these factors on resolution degradation in the presence of phase errors is exhibited.