Recently, we presented the results of a binaural masked detection experiment in which a noise target was temporally embedded within a lead/lag noise masker pair [J. Acoust. Soc. Am. 141, 3639]. The results show that the inter-stimulus interval (ISI) between the masker and its reflection changed the detection threshold significantly. For low ISIs of 2-ms, the average masked detection was -11 dB, but for a greater ISI of 20 ms, the threshold was much higher (-2 dB). In the experiment, masked detection thresholds did not depend on whether the masker lead was on the same side as the target (with the lag on the contralateral side) or the other way round. Different model approaches are presented to simulate the psychophysical results, including a precedence effect (PE) model that was extended using a cepstrum-based method to determine the localization cues for the direct sound of the masker. The PE model is used in conjunction with an EC model and a binaural/monaural detector using optimal frequency-weighting f...