Bilateral cochlear implants (BI-CIs) or a CI for single-sided deafness (SSD; one normally functioning acoustic ear) can partially restore spatial-hearing abilities including sound localization and speech understanding when there are competing sounds. However for these populations, frequency information is not explicitly aligned across the ears, resulting in interaural place-of-stimulation mismatch. This diminishes spatial-hearing abilities because binaural encoding occurs in interaurally frequency-matched neurons. This study examined whether plasticity – the reorganization of central neural pathways over time – can compensate for peripheral interaural place mismatch. We hypothesized differential plasticity across two systems: none for binaural processing but adaptation toward the frequencies delivered by the specific electrodes for sequential pitch perception. Interaural place mismatch was evaluated in 43 human subjects (20 BI-CI and 23 SSD-CI, both sexes) using interaural-time-difference (ITD) discrimination (simultaneous bilateral stimulation), place-pitch ranking (sequential bilateral stimulation), and physical electrode-location estimates from computed-tomography (CT) scans. On average, CT scans revealed relatively little BI-CI interaural place mismatch (26° insertion-angle mismatch), but relatively large SSD-CI mismatch, particularly at the apical end of the array (166° for an electrode tuned to 300 Hz, decreasing to 14° at 7000 Hz). ITD and CT measurements were in agreement, suggesting little binaural-system plasticity to mismatch. The pitch measurements did not agree with the binaural and CT measurements, suggesting plasticity for pitch encoding or procedural biases. The combined results show that binaural processing may be optimized by using CT-scan information, but not pitch measurements, to program the CI frequency allocation to reduce interaural place mismatch.