The suggested method of joint despeckling and set partitioning in hierarchical trees–based compression for degraded multilook synthetic aperture radar (SAR) images uses a fused image as a reference during compression. The fused image itself is formed from intermediate frames (looks) by the logical operation on wavelet coefficients, which are presented in the form of spatial oriented trees (SOTs) of wavelet decomposition. This decomposition is calculated for one and the same region of the Earth’s surface during SAR spacecraft flight. The high-frequency subbands (details) of the fused images contain the smallest wavelet coefficients from different SOTs. The wavelet coefficients related to the low-frequency subband (approximation) are processed by another special logical operation providing a good smoothing. Based on the improved fused image, the best bit rate (optimal operation point) is found by observing the output mean square errors and cross-correlation coefficients between the compressed and reference images. The results of computer modeling and comparison with a few well-known despeckling and compression procedures have shown the superb quality of the proposed method in the sense of different criteria such as peak signal-to-noise ratio, structural similarity, etc.