We have recently proposed a binaural cochlear implant (CI) sound processing strategy inspired by the contralateral medial olivocochlear reflex (the MOC strategy) and shown that it improves intelligibility in steady-state noise (Lopez-Poveda et al., 2016, Ear Hear 37:e138-e148). The aim here was to evaluate possible speech-reception benefits of the MOC strategy for speech maskers, a more natural type of interferer. Speech reception thresholds (SRTs) were measured in six bilateral and two single-sided deaf CI users with the MOC strategy and with a standard (STD) strategy. SRTs were measured in unilateral and bilateral listening conditions, and for target and masker stimuli located at azimuthal angles of (0°, 0°), (−15°, +15°), and (−90°, +90°). Mean SRTs were 2–5 dB better with the MOC than with the STD strategy for spatially separated target and masker sources. For bilateral CI users, the MOC strategy (1) facilitated the intelligibility of speech in competition with spatially separated speech maskers in both unilateral and bilateral listening conditions; and (2) led to an overall improvement in spatial release from masking in the two listening conditions. Insofar as speech is a more natural type of interferer than steady-state noise, the present results suggest that the MOC strategy holds potential for promising outcomes for CI users.