Studies of sound localization use relative or absolute psychoacoustic paradigms. Relative tasks assess acuity by determining the smallest angle separating two sources that subjects can discriminate, the minimum audible angle (MAA), whereas absolute tasks measure subjects' abilities to indicate sound location. It is unclear whether or how measures from the two tasks are related, though the belief that the MAA is specifically related to the precision of absolute localization is common. The present study aimed to investigate the basis of this relationship by comparing the precision of absolute location estimates with a measure of spatial acuity computed from the same data. Three cats were trained to indicate apparent sound source locations that varied in azimuth and elevation via orienting gaze shifts (combined eye and head movements). The precision of these absolute responses, as measured by their standard deviation, was compared with acuity thresholds derived from receiver operating characteristic (ROC) analyses of the cumulative distributions. Surprisingly, the acuity measures were occasionally very poor indicators of absolute localization precision. Incongruent results were attributed to errors in mean accuracy, which are disregarded in analyses of traditional relative tasks. Discussion focuses on the potential for internal biases to affect measures of localization acuity.