Some past work has suggested that lossy compression can be a good denoising tool. Building on this theme, we make the connection that quantization of transform coefficients approximates the operation of Donoho-Johnstone's wavelet thresholding, to conclude that compression (via coefficient quantization) is appropriate for filtering noise from signal. The method of quantization is scale adaptive and is facilitated by a criterion similar to Rissanen's minimum description length principle. Results show that a small number of quantization levels achieves almost the same performance of full precision thresholding, suggesting that denoising is mainly due to the zero-zone and that the full precision of the thresheld coefficients is of secondary importance.