Binaural hearing typically improves speech understanding in difficult listening situations. Cochlear-implant (CI) recipients seek to gain binaural hearing benefits through bilateral implantation. However, the standard of care is currently sequential implantation, possibly with a long difference in the duration of deafness between the ears. Sequential implantation may cause interaural asymmetry in the quality of the signal, which could limit binaural benefits. A range of bilateral CI listeners, from those who experience binaural benefits to those who demonstrate interference, were recruited for this experiment. Listeners attended to one ear and reported digits heard in monotic and dichotic conditions. Perceptual performance and listening effort (via pupillometry) were measured. A control group of normal-hearing listeners were tested and were presented unprocessed, four-, and eight-channel vocoded digits, and the processing was independent across ears. It was hypothesized that attending to a poorer-quality signal in the presence of a better-quality signal would lead to poorer performance than in the monotic condition. Pupillometry was hypothesized to reflect the listener’s ability to perceive the poorer-quality signal in the presence of a better-quality signal. Results will inform strategies to maximize binaural hearing in bilateral CI listeners.