For signal detection and identification, the auditory system needs to integrate sound over time. It is frequently assumed that the quantity ultimately integrated is sound intensity and that the integrator is located centrally. However, we have recently shown that absolute thresholds are much better specified as the temporal integral of the pressure envelope than of intensity, and we proposed that the integrator resides in the auditory pathway's first synapse. We also suggested a physiologically plausible mechanism for its operation, which was ultimately derived from the specific rate of temporal integration, i.e., the decrease of threshold sound pressure levels with increasing duration. In listeners with sensorineural hearing losses, that rate seems reduced, but it is not fully understood why. Here we propose that in such listeners there may be an elevation in the baseline above which sound pressure is effective in driving the system, in addition to a reduction in sensitivity. We test this simple model using thresholds of cats to stimuli of differently shaped temporal envelopes and durations obtained before and after hearing loss. We show that thresholds, specified as the temporal integral of the effective pressure envelope, i.e., the envelope of the pressure exceeding the elevated baseline, behave almost exactly as the lower thresholds, specified as the temporal integral of the total pressure envelope before hearing loss. Thus, the mechanism of temporal integration is likely unchanged after hearing loss, but the effective portion of the stimulus is. Our model constitutes a successful alternative to the model currently favored to account for altered temporal integration in listeners with sensorineural hearing losses, viz., reduced peripheral compression. Our model does not seem to be at variance with physiological observations and it also qualitatively accounts for a number of phenomena observed in such listeners with suprathreshold stimuli.