The human contrast-discrimination function has a curious shape: In addition to rising for increasing contrasts, both positive and negative, it also rises for very low contrasts on either side of zero. It is shown that this rise near zero contrast is not much affected by procedures that increase or decrease the subject's knowledge of the stimulus; this counts against uncertainty as the immediate cause of the elevation near zero contrast. The alternative explanation in terms of a genuine response threshold is shown to be promising when measurements of human contrast discrimination are compared with values calculated from records of neurons in monkey primary visual cortex. The comparison also suggests that the dynamic range of single neurons is lower than that shown psychophysically. It is suggested that having a cortical threshold may be the visual system's way of preventing false positives when there is much stimulus uncertainty. This threshold may also help to explain why quantum efficiencies calculated from detection thresholds are so poor compared with those estimated from the visual system's susceptibility to added noise.