Purpose Listening effort is quickly becoming an important metric for assessing speech perception in less-than-ideal situations. However, the relationship between the construct of listening effort and the measures used to assess it remains unclear. We compared two measures of listening effort: a cognitive dual task and a physiological pupillometry task. We sought to investigate the relationship between these measures of effort and whether engaging effort impacts speech accuracy. Method In Experiment 1, 30 participants completed a dual task and a pupillometry task that were carefully matched in stimuli and design. The dual task consisted of a spoken word recognition task and a visual match-to-sample task. In the pupillometry task, pupil size was monitored while participants completed a spoken word recognition task. Both tasks presented words at three levels of listening difficulty (unmodified, eight-channel vocoding, and four-channel vocoding) and provided response feedback on every trial. We refined the pupillometry task in Experiment 2 (n = 31); crucially, participants no longer received response feedback. Finally, we ran a new group of subjects on both tasks in Experiment 3 (n = 30). Results In Experiment 1, accuracy in the visual task decreased with increased signal degradation in the dual task, but pupil size was sensitive to accuracy and not vocoding condition. After removing feedback in Experiment 2, changes in pupil size were predicted by listening condition, suggesting the task was now sensitive to engaged effort. Both tasks were sensitive to listening difficulty in Experiment 3, but there was no relationship between the tasks and neither task predicted speech accuracy. Conclusions Consistent with previous work, we found little evidence for a relationship between different measures of listening effort. We also found no evidence that effort predicts speech accuracy, suggesting that engaging more effort does not lead to improved speech recognition. Cognitive and physiological measures of listening effort are likely sensitive to different aspects of the construct of listening effort. Supplemental Material https://doi.org/10.23641/asha.16455900.