The masked threshold for a signal is oftentimes lower when the masker is modulated than when it is unmodulated. The difference in masked thresholds is referred to as the modulated–unmodulated difference, or MUD. The purpose of the present study was to follow up on the results of a previous study [Bacon et al., J. Acoust. Soc. Am.101, 1600–1610 (1997)] which showed that the MUD is larger for high than for low signal frequencies, both when the masker is no wider than a critical band (and the processing is solely within channel) and when it is broadband (and the processing may be both within and across channel). The present results indicate that the effects of signal frequency primarily exist only when the modulated masker is modulated at a depth greater than about 0.75, and that at these large depths, thresholds in the presence of the modulated masker are governed largely by forward masking. By far, the effect of signal frequency is larger with the broadband masker than with the critical-band masker, suggesting that there may be an across-channel process whose contribution is greater at high than at low signal frequencies. It is argued here that this across-channel process may be related to psychophysical suppression.