Sensitivity to ongoing interaural temporal disparities (ITDs) was measured using bandpass-filtered pulse trains centered at 4600, 6500, or 9200 Hz. Save for minor differences in the exact center frequencies, those target stimuli were those employed by Majdak and Laback [J. Acoust. Soc. Am. 125, 3903-3913 (2009)]. At each center frequency, threshold ITD was measured for pulse repetition rates ranging from 64 to 609 Hz. The results and quantitative predictions by a cross-correlation-based model indicated that (1) at most pulse repetition rates, threshold ITD increased with center frequency, (2) the cutoff frequency of the putative envelope low-pass filter that determines sensitivity to ITD at high envelope rates appears to be inversely related to center frequency, and (3) both outcomes were accounted for by assuming that, independent of the center frequency, the listeners' decision variable was a constant criterion change in interaural correlation of the stimuli as processed internally. The finding of an inverse relation between center frequency and the envelope rate limitation, while consistent with much prior literature, runs counter to the conclusion reached by Majdak and Laback.