Humans are expert at processing speech but how this feat is accomplished remains a major question in cognitive neuroscience. Capitalizing on the concept of channel capacity, we developed a unified measurement framework to investigate the respective influence of seven acoustic and linguistic features on speech comprehension, encompassing acoustic, sub-lexical, lexical and supra-lexical levels of description. We show that comprehension is independently impacted by all these features, but at varying degrees and with a clear dominance of the syllabic rate. Comparing comprehension of French words and sentences further reveals that when supra-lexical contextual information is present, the impact of all other features is dramatically reduced. Finally, we estimated the channel capacity associated with each linguistic feature and compared them with their generic distribution in natural speech. Our data point towards supra-lexical contextual information as the feature limiting the flow of natural speech. Overall, this study reveals how multilevel linguistic features constrain speech comprehension.