The link between the two phenomena of overshoot and the “severe departure” from Weber's law in intensity discrimination was investigated. Masked thresholds for a brief 6.5-kHz signal were measured in the presence of a notched-noise masker over a range of masker levels. The masker was either gated with the signal (overshoot condition) or was of long duration with the signal temporally centered in it. At mid masker levels, thresholds in the gated condition were substantially higher than in the long-masker condition (overshoot). The overall amount of overshoot and the variation in overshoot as a function of masker level support the view that, even at high frequencies, the overshoot effect is dominated by off-frequency masker components. Pure-tone intensity discrimination tasks were then performed in quiet, and in the presence of the same notched noise in both gated and long-duration noise conditions. It was found that the temporal characteristics of the notched noise and not, as previously thought, the pedestal determined whether or not a severe departure from Weber's law in intensity discrimination was observed. The severe departure from Weber's law was found only in an overshoot condition and then only when the pedestal was presented near masked threshold. This is not in accordance with a previous explanation of the severe departure in terms of two populations of auditory nerve fibers (high- and low-threshold fibers). A further experiment measured psychometric functions for the detection of the 6.5-kHz signal in both gated and long-duration notched noise. It was found that the psychometric function was markedly shallower in an overshoot condition (mid-level gated masker) than in the other conditions. These findings are consistent with a new theory, explaining the severe departure from Weber's law in terms of both the variance in the internal representation of stimuli in an overshoot condition, and the loudness of partially masked signals.