The threshold for detecting a narrow-band noise signal in one or more masking noise bands is higher when the signal and masker bands have the same envelope (correlated condition) than when they have independent envelopes (uncorrelated condition). This comodulation detection difference (CDD) might be caused by perceptual grouping of the signal and masker bands when they are correlated. Alternatively, CDD may occur because, in the uncorrelated condition, the signal can be detected in the dips of the masker. A previous paper [S. J. Borrill and B. C. J. Moore, J. Acoust. Soc. Am. 111, 309-319 (2002)] described results and a model supporting a dip-listening explanation. The model predicted steeper psychometric functions for the correlated than for the uncorrelated condition, a prediction confirmed by experiment 1. In experiment 2, the width of the signal and masker bands was varied. The dip-listening model predicts a small decrease in CDD with increasing bandwidth, while an account based on perceptual grouping predicts a substantial decrease, as across-channel sensitivity to envelope disparity decreases with increasing envelope modulation rate. The CDD was independent of bandwidth. Experiment 3 showed no effect of masker-signal onset asynchrony on CDD, even though asynchrony should reduce perceptual grouping. An explanation of CDD is proposed based on the suppression that has been observed in cochlear mechanics and in the auditory nerve.