This paper used three theoretically different algorithms for reducing noise in event-related potential (ERP) data. It examined the possibility that a hybrid of these methods could show gains in noise reduction beyond that obtained with any single method. The well-known ERP oddball paradigm was used to evaluate three denoising methods: statistical wavelet transform (wavelet-Z), a smooth subspace wavelet filter (wavelet-S), and subspace PCA. The six possible orders of serial application of these methods to the oddball waveforms were compared for efficacy in signal enhancement. It was found that the order was not commutative, with the best results obtained from applying the wavelet-Z first. Comparison of oddball and frequent trials in the grand average and in individual averages showed considerable enhancement of the differences. It was concluded that denoising to remove variance caused by rare sizeable artifacts is best done first, followed by state space PCA and a light-bias model-based wavelet denoising. The ability to detect and distinguish the effects of variables (such as task, drug effects, individual differences, etc.) on ERPs related to human cognition could be considerably advanced using the denoising methods described here.