Covariations of acoustic features provide redundancy in rapidly changing soundscapes: Hearing one feature enables a listener to infer another if these 2 features normally covary. However, it is unknown whether situational demands affect the degree to which covariations influence perceptual inferences. We exploited a perceptual interdependency between modulation rate and frequency and examined, in 6 experiments, whether challenging situations would alter the degree to which people rely on frequency information to make decisions about modulation rate. Participants listened to amplitude-modulated (AM) sounds with modulation rates (∼5 Hz) either decreasing or increasing over time and identified the direction of the rate change. Participants were instructed to ignore carrier frequency, which either decreased or increased (∼1,300 Hz) over time. We observed that participants were more likely to perceive the modulation rate as slowing down when frequency decreased and as speeding up when frequency increased (AM-rate change illusion). The magnitude of the illusion increased when uninformative cues (compared with informative cues) prohibited regulation of attention to sounds, and under distraction introduced by a concurrent visual motion-tracking task. The evidence suggests that the attentional state affects how strongly people rely on featural covariations to make perceptual inferences.