Cat X retinal ganglion cells that can resolve sine gratings of only 2.5 cycles per degree can nevertheless respond reliably to displacements of a grating of approximately 1 minute of arc. This is a form of hyperacuity comparable in magnitude to that seen in human vision. A theoretical analysis of this form of hyperacuity reveals it to be a result of the high gain and low noise of ganglion cells. The hyperacuity expected for the best retinal ganglion cells is substantially better than that observed in behavioral experiments. Thus the brain, rather than improving on the retinal signal-to-noise ratio by pooling signals from many ganglion cells, is unable to make use of all the hyperacuity information present in single ganglion cell responses.