Wavelet based signal processing has become commonplace in the signal processing community over the past decade and wavelet based software tools and integrated circuits are now commercially available. One of the most important applications of wavelets is in removal of noise from signals, called denoising, accomplished by using wavelet coefficient thresholding to separate incoherent noise from the coherent signal. Substantial work in this area was summarized by Donoho and colleagues at Stanford University. They proved basic theorems and developed a variety of algorithms for conventional denoising. However, the application of conventional denoising fails for signals with small signal-to-noise ratios (SNRs). Electrical signals acquired from the human body, called biosignals, commonly have SNRs that are less than 0 dB. Synchronous linear averaging of a large number of acquired data frames is universally used to increase the SNR of weak biosignals. A novel wavelet-based estimator is presented for fast estimation of weak signals, with an application to biosignals. The new estimation algorithm provides a faster rate of convergence to the underlying signal than linear averaging. The algorithm is implemented for processing of auditory brainstem response (ABR) signals acquired in a high noise environment. The ABR is the first 10 ms of an evoked potential response following an acoustic click presented in the ear canal, with SNR below 0 dB. Experimental results with both simulated data and human subjects demonstrate that conventional denoising fails, and that the novel wavelet estimator achieves superior performance to that of linear averaging.