We propose in this paper an efficient and fast wavelet based technique for speckle removal from SAR images. It relies on realistic distributions of the wavelet coefficients which represent mainly speckle noise on the one hand and those that represent the useful signal corrupted by speckle on the other. We propose analytic models for these distributions, and compute their parameters automatically from a given SAR image. The resulting algorithm strongly suppresses speckle, while preserving image details and sharpness.