In recent work, it was proposed to use lossy compression to remove noise from corrupted signals, based on the rationale that a reasonable compression method retains the dominant signal features more than the randomness of the noise. To further understand and substantiate this theory, we first explain why compression (via coefficient quantization) is appropriate for filter thresholding for denoising. That is, denoising is mainly due to the zero-zone and that the full precision of the thresholded coefficients is of secondary importance. Secondly, under the realistic assumption that wavelet coefficients follow a Generalized Gaussian distribution, we derive an optimal threshold value (and thus the zero-zone width) from minimizing the mean squared error among soft-threshold estimators. We propose an adaptive threshold which is easy to compute and nearly optimal. Thirdly, along with the chosen zero-zone, we use Rissanen's Minimum Description Length (MDL) principle to quantize outside of the zero-zone. Lastly, experimental results on noisy images show that the proposed compression method does indeed remove noise and improve the image quality.