The accurate reproduction of coloured images requires not only an understanding of device behaviour but also of the differences in colour appearance between the source and destination media. These differences can be compensated by transforming the image data into a perceptual colour appearance space, but the problem still remains of how best to convert the gamut of colours in the original to make best use of the colour gamut of the reproduction device. Some shortcomings of existing gamut mapping algorithms are described and a five-stage transform for optimum image reproduction is proposed.