The relative importance of individual frequency regions for speech intelligibility has been firmly established for broadband auditory-only (AO) conditions. Yet, speech communication often takes place face-to-face. This study tested the hypothesis that under auditory-visual (AV) conditions, where visual information is redundant with high-frequency auditory cues, lower frequency regions will increase in relative importance compared to AO conditions. Frequency band-importance functions for consonants were measured for eight hearing-impaired and four normal-hearing listeners. Speech was filtered into four 1/3-octave bands each separated by an octave to minimize energetic masking. On each trial, the signal-to-noise ratio (SNR) in each band was selected randomly from a 10-dB range. AO and AV band-importance functions were estimated using three logistic-regression analyses: a primary model relating performance to the four independent SNRs; a control model that also included band-interaction terms; and a different set of four control models, each examining one band at a time. For both listener groups, the relative importance of the low-frequency bands increased under AV conditions, consistent with earlier studies using isolated speech bands. All three analyses showed similar results, indicating the absence of cross-band interactions. These results suggest that accurate prediction of AV speech intelligibility may require different frequency-importance functions than for AO conditions.