We measured responses of macaque ganglion cells as a function of contrast in a simple hyperacuity task, detection of displacement of an achromatic edge. Responses of ganglion cells of the magnocellular (MC) pathway were much more vigorous than those of cells of the parvocellular (PC) pathway. From the variability in the number of impulses in the response as compared with the distribution of impulses in maintained activity, it was possible to generate receiver operating characteristics for cells of the two pathways, and to predict individual cells' capability to detect a displacement with 75% probability. On comparing cell sensitivities to human psychophysical thresholds (75% probability of correct identification of displacement direction) at an equivalent retinal eccentricity (approximately 6 degrees), we found that one or two additional impulses in two MC pathway cells would suffice to support an ideal detector underlying psychophysical performance, at all contrast levels. Many more PC pathway cells would be required, especially at low contrasts. The much higher signal-to-noise ratio in the MC pathway relative to the PC pathway indicates that the MC pathway is likely to support this and other hyperacuity tasks.