Hyperacuity thresholds for disparity, motion displacement and relative width (widths less than 10 min arc) were measured as a function of the separation between test and reference targets for separations ranging from 18-288 min arc. All three thresholds were similar in magnitude, and showed a nearly identical rise with increasing separation. Nevertheless, eccentricity, not separation, is the variable limiting all of these thresholds. This point is underscored by the fact that relative width judgments, made by comparing the narrow widths separating two pairs of lines (test and reference widths), are equally good without the reference pair. The most precise foveal judgments of stereo and motion do require a visible reference target because the observer cannot otherwise distinguish between oculomotor "jitter" and target-driven changes in disparity or motion. At eccentricities greater than 2 deg, stereo and motion thresholds for a single unreferenced line (150 msec duration) were equal to the referenced thresholds, presumably because the oculomotor noise is less than the positional uncertainty associated with these peripheral loci.