The alignment of nonius targets can be judged with the same precision as the alignment of vernier targets for some target configurations. We measured dichoptic and monocular hyperacuity thresholds as a function of the separation between the target lines. At separations above a critical value (30-60 arcmin), monocular and dichoptic thresholds were identical and increased as a power function of line separation. At smaller separations, the dichoptic thresholds were 0.6-0.7 arcmin, independent of separation, and significantly higher than the comparable monocular thresholds. The dichoptic results can be modeled as the sum of two sources of noise: (1) intrinsic positional uncertainty, which depends on line separation and is common to both dichoptic and monocular judgments, and (2) disjunctive fluctuations in convergence. It seems likely that the mechanism that limits the precision of vernier acuity has its locus at a point in the visual pathways after the signals from the two eyes have been combined.