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A novel algorithm for the lossless compression of hyperspectral sounding data is presented. The algorithm rests upon an efficient technique for three-dimensional image band reordering. The technique is based on a correlation factor. The correlation-based band ordering gives 5% higher compression ratios than natural ordering does. On the other hand, the obtained compression ratios are within a percent of those produced by optimal ordering, but the computational time is much lower compared to the optimal ordering. The low computational complexity of the algorithm is based on the use of correlation for the band ordering. Moreover, the algorithm results in 7% to 12% improvement over fast nearest neighbor reordering scheme versions of JPEG-LS and the context-based adaptive lossless image codec algorithms.