Hierarchical models of auditory processing often posit that optimal stimuli, i.e., those eliciting a maximal neural response, will increase in bandwidth and decrease in modulation rate as one ascends the auditory neuraxis. Here, we tested how bandwidth and modulation rate interact at several loci along the human central auditory pathway using functional MRI in a cardiac-gated, sparse acquisition design. Participants listened passively to both narrowband (NB) and broadband (BB) carriers (1/4- or 4-octave pink noise), which were jittered about a mean sinusoidal amplitude modulation rate of 0, 3, 29, or 57 Hz. The jittering was introduced to minimize stimulus-specific adaptation. The results revealed a clear difference between spectral bandwidth and temporal modulation rate: sensitivity to bandwidth (BB > NB) decreased from subcortical structures to nonprimary auditory cortex, whereas sensitivity to slow modulation rates was largest in nonprimary auditory cortex and largely absent in subcortical structures. Furthermore, there was no parametric interaction between bandwidth and modulation rate. These results challenge simple hierarchical models, in that BB stimuli evoked stronger responses in primary auditory cortex (and subcortical structures) rather than nonprimary cortex. Furthermore, the strong preference for slow modulation rates in nonprimary cortex demonstrates the compelling global sensitivity of auditory cortex to modulation rates that are dominant in the principal signals that we process, e.g., speech.