We propose a novel method for simultaneous speckle reduction and data compression based on shrinking, quantizing and coding the wavelet packet coefficients of the logarithmically transformed image. A fast algorithm is used to find the best wavelet packet basis in the rate-distortion sense from the entire library of admissible wavelet packet bases. Soft-thresholding in wavelet domain can significantly suppress the speckles of the synthetic aperture radar (SAR) images while maintaining bright reflections for subsequent detection and recognition. Optimal bit allocation, quantization and entropy coding achieve the goal of compression while maintaining the fidelity of the SAR image.