Intensity-discrimination limens (IDLs) and auditory brainstem responses (ABRs) were measured as a function of stimulus intensity in 6 cochlear implant (CI) and 8 normal-hearing (NH) listeners. Pulse-train stimuli were delivered electrically to the auditory nerve in CI listeners and acoustically in NH listeners. In CI listeners, the IDLs expressed as Weber fractions decreased monotonically with increasing intensity. In NH listeners, a nonmonotonic IDL function showing a peak a midintensities was observed. ABR wave amplitudes increased regularly with intensity only in CI listeners. Results support the notion that the slight decrease in Weber's fractions with increasing sound intensity--generally referred to as "the near-miss to Weber's law"--is subtended by retrocochlear processes, whereas the increase in Weber's fractions at midlevels--known as "the severe departure from Weber's law"--originates in cochlear mechanisms.