In a complex auditory scene, location in space is one of several acoustic features that permit listeners to segregate competing sequences of sounds into discrete perceptual streams. Nevertheless, the spatial acuity of stream segregation is unknown. Moreover, it is not clear whether this is really a spatial effect or whether it reflects a binaural process that only indirectly involves space. We employed "rhythmic masking release" as an objective measure of spatial stream segregation. That task revealed spatial acuity nearly as fine as listeners' discriminations of static locations (i.e., their minimum audible angles). Tests using low-pass, high-pass, and varying-level conditions in the horizontal dimension demonstrated that binaural difference cues provide finer acuity than does any monaural cue and that low-frequency interaural delay cues give finer acuity than do high-frequency interaural level differences. Surprisingly, stream segregation in the vertical dimension, where binaural difference cues are negligible, could be nearly as acute as that in the horizontal dimension. The results show a common spatial underpinning to performance. Nevertheless, a dissociation across conditions between localization acuity and masking-release thresholds suggests that spatial stream segregation is accomplished by brain systems discrete from those responsible for sound-localization judgments.