Speech is often degraded by environmental noise or hearing impairment. People can compensate for degradation, but this requires cognitive effort. Previous research has identified frontotemporal networks involved in effortful perception, but materials in these works were also less intelligible, and so it is not clear whether activity reflected effort or intelligibility differences. We used functional magnetic resonance imaging to assess the degree to which spoken sentences were processed under distraction and whether this depended on speech quality even when intelligibility of degraded speech was matched to that of clear speech (close to 100%). On each trial, male and female human participants either attended to a sentence or to a concurrent multiple object tracking (MOT) task that imposed parametric cognitive load. Activity in bilateral anterior insula reflected task demands; during the MOT task, activity increased as cognitive load increased, and during speech listening, activity increased as speech becam...