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The techniques proposed for joint denoising and compression of images corrupted with additive white Gaussian noise are mostly based on Rissanen's minimum description length principle and tend to operate at a particular point (or a set of points) on the rate-distortion curve. These offer some compression along with denoising, but not a practical encoding solution. This paper suggests a simple adaptation of the zero-zone and the reconstruction levels of the uniform threshold quantizer based on the noise level in the image and the required compression rate. Context-based classification is also described for the noisy coefficients, and this raises the performance of the subband coder significantly.