Data in medical images is very large and therefore for storage and/or transmission of these images, compression is essential. A method is proposed which provides high compression ratios for radiographic images with no loss of diagnostic quality. In the approach an image is first compressed at a high compression ratio but with loss, and the error image is then compressed losslessly. The resulting compression is not only strictly lossless, but also expected to yield a high compression ratio, especially if the lossy compression technique is good. A neural network vector quantizer (NNVQ) is used as a lossy compressor, while for lossless compression Huffman coding is used. Quality of images is evaluated by comparing with standard compression techniques available.