Based on Kimura’s (1967) anatomical model of dichotic listening, the right ear has a slight advantage (REA) or performance asymmetry, compared with the left ear. This is due to left hemisphere dominance for language, which receives direct input from the right ear. Accurate performance on dichotic tests relies on sensory organization and memory; however, there is little evidence regarding the impact of increasing cognitive demands (i.e., number of items for recall) on auditory performance asymmetries in mature auditory systems. This study investigated 42 participants’ auditory perceptual and working memory abilities (e.g., forward and reverse digit spans, dichotic digits test, and directed ear dichotic digits test) to explore the relationships among cognitive demanded and performance asymmetries. Repeated measures ANOVA showed a significant effect for directed ear and digit list length. In addition, a priori comparison indicated significant performance asymmetry, with persistent REA when listening demands exceeded an individual’s auditory memory capacity. No significant performance differences were identified for digit list lengths relative to, or below an individual’s simple memory capacity. Overall, the study found the right ear tends to show better performance on dichotic listening tasks, even in adults, when the number of digits exceeded the participants’ digit span capacity.