We examined the mechanisms that underlie 'band-suppression' amplitude modulation selectivity in the auditory midbrain of anurans. Band-suppression neurons respond well to low (5-10 Hz) and high (>70 Hz) rates of sinusoidal amplitude modulation, but poorly, if at all, to intermediate rates. The effectiveness of slow rates of sinusoidal amplitude modulation is due to the long duration of individual 'pulses'; short-duration pulses (<10 ms) failed to elicit spikes when presented at 5-10 pulses s(-1). Each unit responded only after a threshold number of pulses (median=3, range=2-5) were delivered at an optimal rate. The salient stimulus feature was the number of consecutive interpulse intervals that were within a cell-specific tolerance. This interval-integrating process could be reset by a single long interval, even if preceded by a suprathreshold number of intervals. These findings indicate that band-suppression units are a subset of interval-integrating neurons. Band-suppression neurons differed from band-pass interval-integrating cells in having lower interval-number thresholds and broader interval tolerance. We suggest that these properties increase the probability of a postsynaptic spike, given a particular temporal pattern of afferent action potentials in response to long-duration pulses, i.e., predispose them to respond to slow rates of amplitude modulation. Modeling evidence is provided that supports this conclusion.