A spectral gamut-mapping algorithm is introduced that works well for printers with a large number of inks. It finds the best mapping onto the convex hull of the printer spectral gamut while preserving color defined in CIE XYZ as much as possible. The technique employs a non-negative least-square fit. Since the gamut-mapping algorithm depends on the common assumption that the gamut is convex, an experimental study of the degree of gamut concavity is conducted. It finds that there is a significant amount of concavity, and that that the degree does not appear to change much as the number of inks is increased. Finally, the performance of the gamut-mapping algorithm and gamut coverage in spectral space is compared for 3-, 4-, 5- and 6-ink printers using both synthetic ink models and real ink data.