Wavelet shrinkage denoising provides a novel method of reducing noise in signals. The author demonstrates 1D and 2D examples, tests the performance of various ideal and practical Fourier- and wavelet-based denoising procedures, and makes recommendations for practitioners. It is is concluded that it is unlikely that one particular wavelet shrinkage denoising procedure will be suitable, no less optimal, for all practical problems. However, it is likely that there will be many practical problems, for which after appropriate experimentation, wavelet-based denoising with either hard or soft thresholding proves to be the most effective procedure. Using wavelet-based denoising of the log-periodogram to estimate the power spectrum might prove to be one such important application with great promise for further development.