The auditory brainstem response (ABR) is an integral clinical metric for the estimation of hearing threshold, assessment of the neurological integrity of the auditory system, and most commonly, screening for hearing loss in newborns and babies. However, the ABR response can be constrained by low signal-to-noise ratios (SNR) precluding accurate and reliable responses. Artefact rejection (AR) is one technique used to improve the SNR by allowing signal averaging to continue only if the peak amplitude of the response is below a defined limit. The current study investigates the effect of Bayesian weighting and AR level upon the efficiency of noise reduction across 26 babies referred from the English Newborn Hearing Screening program. ABR recordings using an Interacoustics Eclipse were evaluated for 5 AR levels and 2 AR levels with Bayesian averaging. Strict AR levels are optimal when noise is low; whereas, more lenient AR levels are more efficient when noise is high. Bayesian averaging can facilitate increased efficiency as noise levels increase. This suggests that the use of Bayesian weighting available in the Eclipse offers additional efficiency for reducing the effects of noise on ABR recordings.