The potential contribution of the peripheral auditory efferent system to our understanding of speech in a background of competing noise was studied using a computer model of the auditory periphery and assessed using an automatic speech recognition system. A previous study had shown that a fixed efferent attenuation applied to all channels of a multi-channel model could improve the recognition of connected digit triplets in noise [G. J. Brown, R. T. Ferry, and R. Meddis, J. Acoust. Soc. Am. 127, 943-954 (2010)]. In the current study an anatomically justified feedback loop was used to automatically regulate separate attenuation values for each auditory channel. This arrangement resulted in a further enhancement of speech recognition over fixed-attenuation conditions. Comparisons between multi-talker babble and pink noise interference conditions suggest that the benefit originates from the model's ability to modify the amount of suppression in each channel separately according to the spectral shape of the interfering sounds.