We investigate Wiener filtering of wavelet coefficients for signal denoising. Empirically designed wavelet-domain Wiener filters outperform many other denoising algorithms based on wavelet thresholding. However, up to now, it has not been clear how to choose the signal model used to design the filter, because the effect of model selection on the filter performance is difficult to understand. By analyzing the error involved in the Wiener filter designed with an empirically obtained signal model, we show that hard thresholding is typically outperformed by a Wiener filter designed in an alternate wavelet domain. Our analysis furthermore provides a method for selecting the various parameters involved in a wavelet-domain Wiener filtering scheme.