Although the rounded-exponential (roex) filter has been successfully used to represent the magnitude response of the auditory filter, recent studies with the roex(p, w, t) filter reveal two serious problems: the fits to notched-noise masking data are somewhat unstable unless the filter is reduced to a physically unrealizable form, and there is no time-domain version of the roex(p, w, t) filter to support modeling of the perception of complex sounds. This paper describes a compressive gammachirp (cGC) filter with the same architecture as the roex(p, w, t) which can be implemented in the time domain. The gain and asymmetry of this parallel cGC filter are shown to be comparable to those of the roex(p, w, t) filter, but the fits to masking data are still somewhat unstable. The roex(p, w, t) and parallel cGC filters were also compared with the cascade cGC filter [Patterson et al., J. Acoust. Soc. Am. 114, 1529-1542 (2003)], which was found to provide an equivalent fit with 25% fewer coefficients. Moreover, the fits were stable. The advantage of the cascade cGC filter appears to derive from its parsimonious representation of the high-frequency side of the filter. It is concluded that cGC filters offer better prospects than roex filters for the representation of the auditory filter.