We measured Weber fractions for discriminating the speed of cyclopean gratings and Weber fractions for discriminating the speed of luminance gratings. Of our 14 observers, five were unable to see the cyclopean grating sufficiently well to discriminate its speed. One observer experienced great difficulty in discriminating the speed of cyclopean gratings, even though her threshold for detecting cyclopean gratings was low, and even though she discriminated the speed of luminance gratings on the basis of the task-relevent variable. But several observers based their speed discriminations on trial-to-trial variations of the task-relevent variable while ignoring associated trial-to-trial variations in all task-irrelevant variables (specifically: displacement; temporal frequency; spatial frequency; and presentation duration). We conclude that the visual systems of these observers contain a specialized neural mechanism for the speed of cyclopean gratings that supports acute discriminations of speed (Weber fractions were as low as 0.05-0.07).