Abstract <p>The paper investigates an iterative approximation-based method of compressing discrete multispectral images. Less thinned multispectral images are used to approximate more thinned ones, the degree of thinning decreasing in an iterrative fashion. When a set of thinned multispectral images is used, the data redundency is eliminated by using nonredundant nested covers consisted of specially reduced thinned images. Approximation errors are rounded and stored. The paper considers an algorithm of detection and effective representation of degenerate subsets of rounded iterative approximation errors. The algotithm allows more efficient representation of rounded error subsets and higher data compression ratios. The computational experiment confirms a considerable increase in efficiency of the iterative approximation-based method of discrete multispectral data compression.</p>