Two experiments investigated the conditions under which cognitive load exerts an effect on the acuity of speech perception. These experiments extend earlier research by using a different speech perception task (four-interval oddity task) and by implementing cognitive load through a task often thought to be modular, namely, face processing. In the cognitive-load conditions, participants were required to remember two faces presented before the speech stimuli. In Experiment 1, performance in the speech-perception task under cognitive load was not impaired in comparison to a no-load baseline condition. In Experiment 2, we modified the load condition minimally such that it required encoding of the two faces simultaneously with the speech stimuli. As a reference condition, we also used a visual search task that in earlier experiments had led to poorer speech perception. Both concurrent tasks led to decrements in the speech task. The results suggest that speech perception is affected even by loads thought to be processed modularly, and that, critically, encoding in working memory might be the locus of interference.