Two criteria for selecting ink sets for six-color lithographic printing are discussed. The first is the volume, in CIELAB space, of an approximation of the gamut. The second is the number of pixels within a digital image (or images) whose colors are contained within the approximate gamut.In order to obtain a balance between accuracy and efficiency, the different steps in the process are prioritized according to their impact on accuracy, their requirements for specialized measurements, and the computational load they create. Factors which have a first-order impact on accuracy are measured, while factors with higher-order, less controlling, impact are computed or estimated.Overprints of two or more colorants are estimated using a spectral model, rather than measured from printed samples. Combinations of inks on the gamut surface which contain intermediate amounts of inks are estimated using a spectrally-sharpened wideband model. The estimation is performed in a space in which subtractive colorants behave more linearly than density.A convex hull of the gamut is constructed in the linear space, using Computer Graphics routines. Through repeated bisection, the surface of the gamut is sampled in the linear space. The coordinates of the vertices are then transformed into CIELAB color space, for display, comparison, and analysis.