Languages vary in their number of color terms. A widely accepted theory proposes that languages evolve, acquiring color terms in a stereotyped sequence. This theory, by Berlin and Kay (BK), is supported by analyzing best exemplars ("focal colors") of basic color terms in the World Color Survey (WCS) of 110 languages. But the instructions of the WCS were complex and the color chips confounded hue and saturation, which likely impacted focal-color selection. In addition, it is now known that even so-called early-stage languages nonetheless have a complete representation of color distributed across the population. These facts undermine the BK theory. Here we revisit the evolution of color terms using original color-naming data obtained with simple instructions in Tsimane', an Amazonian culture that has limited contact with industrialized society. We also collected data in Bolivian-Spanish speakers and English speakers. We discovered that information theory analysis of color-naming data was not influenced by color-chip saturation, which motivated a new analysis of the WCS data. Embedded within a universal pattern in which warm colors (reds, oranges) are always communicated more efficiently than cool colors (blues, greens), as languages increase in overall communicative efficiency about color, some colors undergo greater increases in communication efficiency compared to others. Communication efficiency increases first for yellow, then brown, then purple. The present analyses and results provide a new framework for understanding the evolution of color terms: what varies among cultures is not whether colors are seen differently, but the extent to which color is useful.