A computer simulation was performed to investigate optimal four- and five-ink sets in order to minimize color inconstancy while maintaining a large color gamut. The effect of including a spectrally-flat black ink on color constancy was explored. The relationship between ink shape and the color constancy of prints was also analyzed. The results show that the ink shape in the middle wavelength region is very important for the color constancy of prints. The minimum and maximum color inconstancy indices that the different ink sets can achieve, which were optimized by different objective functions, were explored. The results show that color constancy can be improved by both ink design and lookup table creation.