We systematically determined which spectrotemporal modulations in speech are necessary for comprehension by human listeners. Speech comprehension has been shown to be robust to spectral and temporal degradations, but the specific relevance of particular degradations is arguable due to the complexity of the joint spectral and temporal information in the speech signal. We applied a novel modulation filtering technique to recorded sentences to restrict acoustic information quantitatively and to obtain a joint spectrotemporal modulation transfer function for speech comprehension, the speech MTF. For American English, the speech MTF showed the criticality of low modulation frequencies in both time and frequency. Comprehension was significantly impaired when temporal modulations <12 Hz or spectral modulations <4 cycles/kHz were removed. More specifically, the MTF was bandpass in temporal modulations and low-pass in spectral modulations: temporal modulations from 1 to 7 Hz and spectral modulations <1 cycles/kHz were the most important. We evaluated the importance of spectrotemporal modulations for vocal gender identification and found a different region of interest: removing spectral modulations between 3 and 7 cycles/kHz significantly increases gender misidentifications of female speakers. The determination of the speech MTF furnishes an additional method for producing speech signals with reduced bandwidth but high intelligibility. Such compression could be used for audio applications such as file compression or noise removal and for clinical applications such as signal processing for cochlear implants.