Determining a spectral gamut of a device by designating a spanning set of samples which span the spectral gamut. A first crude spanning set of samples is established by specifying one or more corresponding device values in a device color space. The first crude spanning set is refined by processing a plurality of new samples in a predetermined order. The processing includes, for each new sample, determining if the new sample differs in an objective function value by more than a predetermined threshold from all samples in the first crude spanning set and adding the new sample to the first crude spanning set if the new sample differs in the objective function value by more than the predetermined threshold. The resulting first crude spanning set is designated as the spanning set of samples.