Acoustic simulations were used to study the contributions of spatial hearing that may arise from combining a cochlear implant with either a second implant or contralateral residual low-frequency acoustic hearing. Speech reception thresholds (SRTs) were measured in twenty-talker babble. Spatial separation of speech and noise was simulated using a spherical head model. While low-frequency acoustic information contralateral to the implant simulation produced substantially better SRTs there was no effect of spatial cues on SRT, even when interaural differences were artificially enhanced. Simulated bilateral implants showed a significant head shadow effect, but no binaural unmasking based on interaural time differences, and weak, inconsistent overall spatial release from masking. There was also a small but significant non-spatial summation effect. It appears that typical cochlear implant speech processing strategies may substantially reduce the utility of spatial cues, even in the absence of degraded neural processing arising from auditory deprivation.