We present a new image compression method for very-high-quality lossy compression. This method caters for image data in regimes of (a) detector imperfections, which motivates a robust approach based on the median transform; and (b) noise, which is explicitly sought and separated out, since noise is inherently noncompressible. An in-depth assessment is carried out on real data, relative to the standard JPEG compression method. Comparable visual quality is based on 260:1 compression with the new method, and 40:1 compression with JPEG. The assessment procedure, based on the astronomical images used, is an objective approach for determining very-high-quality visual reconstructions. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 38–45, 1998