Successful speech communication often requires selective attention to a target stream amidst competing sounds, as well as the ability to switch attention among multiple interlocutors. However, auditory attention switching negatively affects both target detection accuracy and reaction time, suggesting that attention switches carry a cognitive cost. Pupillometry is one method of assessing mental effort or cognitive load. Two experiments were conducted to determine whether the effort associated with attention switches is detectable in the pupillary response. In both experiments, pupil dilation, target detection sensitivity, and reaction time were measured; the task required listeners to either maintain or switch attention between two concurrent speech streams. Secondary manipulations explored whether switch-related effort would increase when auditory streaming was harder. In experiment 1, spatially distinct stimuli were degraded by simulating reverberation (compromising across-time streaming cues), and target-masker talker gender match was also varied. In experiment 2, diotic streams separable by talker voice quality and pitch were degraded by noise vocoding, and the time alloted for mid-trial attention switching was varied. All trial manipulations had some effect on target detection sensitivity and/or reaction time; however, only the attention-switching manipulation affected the pupillary response: greater dilation was observed in trials requiring switching attention between talkers.