One of the most fundamental functions of the visual system is to code the positions of objects. Physiological studies, especially those using fMRI, widely assume that the location of the peak retinotopic activity generated in the visual cortex by an object is the position assigned to that object—this is the simplified version of the labelled-line hypothesis. Here, we employed a novel technique to compare population level BOLD responses to moving and stationary objects and found that this widely-held version of the labelled-line hypothesis is false. By spatially correlating population responses to moving and stationary stimuli in slightly different positions, we found that the voxel population in primary visual cortex can discriminate the positions of objects separated by less than 0.5 deg visual angle (approximately 0.3 mm cortical distance at ∼20 deg eccentricity). This is at or better than the ability of subjects to psychophysically classify the positions of the stimuli. More surprisingly, the population of voxels in motion area MT+—a visual area traditionally thought to be only coarsely retinotopic—is able to discriminate objects separated by approximately 2 deg visual angle, revealing precise topographic coding of object position. The results further show that the position assigned to a pattern is not simply dictated by the peak response; changes at the edges of the population response carry significant position information without altering the peak response. Therefore, visually coded location is not conveyed by the topographic location of a peak response, but by the activity across a population of neurons.