A fundamental challenge of binocular vision is that images of an object generally project to different positions on the two retinae (binocular disparity). Neurons in visual cortex show two distinct types of tuning to disparity: position and phase disparity, due to differences in receptive field location and profile respectively. However, phase disparities do not occur in natural stimuli. Why, then, should the brain devote computational resources to encoding it? An analysis of population responses in model neurons suggests an answer: phase disparity detectors help work out which feature in the left eye corresponds to a given feature in the right. This correspondence problem is challenging because of false matches: regions of the image which look similar but do not correspond to the same physical object. Phase-disparity neurons tend to be more strongly activated by false matches. Thus, they may act as "lie detectors", enabling the true correspondence to be deduced by a process of elimination. This could be implemented simply with mutual inhibition in the visual cortex.