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This paper proposes a new method for chromosome image compression based on an important characteristic of these images: the regions of interest (ROIs) to cytogeneticists for evaluation and diagnosis are well determined and segmented. Such information is utilized to advantage in our compression algorithm, which combines lossless compression of chromosome ROIs with lossy-to-lossless coding of the remaining image parts. This is accomplished by first performing a differential operation on chromosome ROIs for decorrelation, followed by critically sampled integer wavelet transforms on these regions and the remaining image parts. The well-known set partitioning in hierarchical trees (SPIHT) (Said and Perlman, 1996) algorithm is modified to generate separate embedded bit streams for both chromosome ROIs and the rest of the image that allow continuous lossy-to-lossless compression of both (although lossless compression of the former is commonly used in practice). Experiments on two sets of sample chromosome spread and karyotype images indicate that the proposed approach significantly outperforms current compression techniques used in commercial karyotyping systems and JPEG-2000 compression, which does not provide the desirable support for lossless compression of arbitrary ROIs.