Human listeners understand spoken language across a variety of rates, but when speech is presented three times or more faster than its usual rate, it becomes unintelligible. How the brain achieves such tolerance and why speech becomes unintelligible above certain rates is still unclear. We addressed these questions using electrocorticography (ECoG) recordings in 7 epileptic patients (two female). Patients rated the intelligibility of sentences presented at the original rate (100%), speeded rates (33% or 66% of the original sentence duration) and a slowed rate (150%). We then examined which parameters of the neural response covary with the transition from intelligible to unintelligible speech. Specifically, we asked whether neural responses: 1) track the acoustic envelope of the incoming speech; 2) “scale” with speech rate, i.e. whether neural responses elicited by slowed and speeded sentences can be linearly scaled to match the responses to the original sentence. Behaviorally, intelligibility was at ceiling for speech rates of 66% and above, but dropped significantly for the 33% rate. At the neural level, Superior Temporal Gyrus regions (STG) in close proximity to A1 (‘low-level’) tracked the acoustic envelope and linearly scaled with the input across all speech rates, irrespective of intelligibility. In contrast, secondary auditory areas in the STG as well as the inferior frontal gyrus and angular gyrus (‘high-level’) tracked the acoustic envelope and linearly scaled with input only for intelligible speech. These results help reconcile seemingly contradictory previous findings and provide better understanding of how information processing unfolds along the cortical auditory hierarchy.