When speech is degraded, word report is higher for semantically coherent sentences (e.g., her new skirt was made of denim ) than for anomalous sentences (e.g., her good slope was done in carrot ). Such increased intelligibility is often described as resulting from “top–down” processes, reflecting an assumption that higher-level (semantic) neural processes support lower-level (perceptual) mechanisms. We used time-resolved sparse fMRI to test for top–down neural mechanisms, measuring activity while participants heard coherent and anomalous sentences presented in speech envelope/spectrum noise at varying signal-to-noise ratios (SNR). The timing of BOLD responses to more intelligible speech provides evidence of hierarchical organization, with earlier responses in peri-auditory regions of the posterior superior temporal gyrus than in more distant temporal and frontal regions. Despite Sentence content × SNR interactions in the superior temporal gyrus, prefrontal regions respond after auditory/perceptual regions. Although we cannot rule out top–down effects, this pattern is more compatible with a purely feedforward or bottom–up account, in which the results of lower-level perceptual processing are passed to inferior frontal regions. Behavioral and neural evidence that sentence content influences perception of degraded speech does not necessarily imply “top–down” neural processes.