Color naming in the world’s languages has traditionally been viewed as reflecting either a universal set of focal colors, or linguistic relativity. Recently, a different view has gained support: color naming may be accounted for in terms of the overall shape of perceptual color space. Here, we show that the new shape-based perspective can clarify which languages have color-naming systems that deviate from what universal forces would predict. Specifically, we find that the color-naming systems of two languages that have been held to counterexemplify universals of color naming—Pirahã and Warlpiri—are in fact consistent with the structure of color space. In contrast, two other languages that have not yet been the focus of much attention—Karajá and Waorani—are apparently inconsistent with that structure in a substantial way. We propose that the notion of ‘fit to the shape of color space’ provides a useful and objective means of determining which languages have genuinely unusual color-naming systems.