Using a cochlear implant simulator, Stone and Moore [J. Acoust. Soc. Am. 114, 1023-1034 (2003)] reported that wideband fast-acting compression led to poorer intelligibility than slow-acting compression in a competing speech task. Compression speed was varied by using different pairs of attack and release times. In the first experiment reported here, it is shown that attack times less than about 2 ms in a wideband compressor are deleterious to intelligibility. In experiment 2, fast wideband compression was applied to the target and background either before or after mixing. The former reduced the modulation depth of each signal but maintained the independence between the two signals, while the latter introduced "comodulation." Using simulations with 6 and 11 channels, intelligibility was higher when compression was applied before mixing. In experiment 3, wideband compression was compared with multichannel compression; the latter led to reduced comodulation effects. For 6 channels, the position of the compressor, either wideband or within each channel, had no effect on intelligibility. For 11 channels, channel compression severely degraded intelligibility compared to wideband compression, presumably because of the greater reduction of across-channel contrasts. Overall, caution appears necessary in the use of fast-acting compression in cochlear implants, so as to preserve intelligibility.