There are an increasing number of bilateral and single-sided-deafness cochlear-implant (CI) users who hope to achieve improved spatial-hearing abilities through access to sound in both ears. It is, however, unclear how speech is processed when inputs are functionally asymmetrical, which may have an impact on spatial-hearing abilities. Therefore, functionally asymmetrical hearing was controlled and parametrically manipulated using a channel vocoder as a CI simulation. In Experiment 1, normal-hearing (NH) listeners performed a dichotic listening task (i.e., selective attention to one ear, ignoring the other) using asymmetrical signal degradation. Spectral resolution varied independently in each ear (4, 8, 16 channels, and unprocessed control). Performance decreased with decreasing resolution in the target ear and increasing resolution in the interferer ear. In Experiment 2, these results were replicated using a divided attention task (attend to both ears, report one after sentence completion) in both NH and bilateral CI listeners, although overall performance was lower than in Experiment 1. In Experiment 3, frequency-to-place mismatch simulated shallow CI insertion depths (0, 3, 6-mm shifts, and unprocessed control). Performance mostly decreased with increasing shift in the target ear and decreasing shift in the interferer ear; however, performance nonmonotonicities occurred. The worst performance occurred when the shift matched across ears, suggesting that pitch similarity increases difficulty. The results show that it is more difficult to attend an ear that is relatively degraded or distorted, which may set spatial-hearing limitations for CI users when trying to attend to a target in complex auditory scenes.