It has been recently shown that cochlear implant users could enjoy better speech reception in noise and enhanced spatial unmasking with binaural audio processing inspired by the inhibitory effects of the contralateral medial olivocochlear (MOC) reflex on compression [Lopez-Poveda, Eustaquio-Martin, Stohl, Wolford, Schatzer, and Wilson (2016). Ear Hear. 37, e138-e148]. The perceptual evidence supporting those benefits, however, is limited to a few target-interferer spatial configurations and to a particular implementation of contralateral MOC inhibition. Here, the short-term objective intelligibility index is used to (1) objectively demonstrate potential benefits over many more spatial configurations, and (2) investigate if the predicted benefits may be enhanced by using more realistic MOC implementations. Results corroborate the advantages and drawbacks of MOC processing indicated by the previously published perceptual tests. The results also suggest that the benefits may be enhanced and the drawbacks overcome by using longer time constants for the activation and deactivation of inhibition and, to a lesser extent, by using a comparatively greater inhibition in the lower than in the higher frequency channels. Compared to using two functionally independent processors, the better MOC processor improved the signal-to-noise ratio in the two ears between 1 and 6 decibels by enhancing head-shadow effects, and was advantageous for all tested target-interferer spatial configurations.