Color vision supports two distinct visual functions: discrimination and constancy. Discrimination requires that the visual response to distinct objects within a scene be different. Constancy requires that the visual response to any object be the same across scenes. Across changes in scene, adaptation can improve discrimination by optimizing the use of the available response range. Similarly, adaptation can improve constancy by stabilizing the visual response to any fixed object across changes in illumination. Can common mechanisms of adaptation achieve these two goals simultaneously? We develop a theoretical framework for answering this question and present several example calculations. In the examples studied, the answer is largely yes when the change of scene consists of a change in illumination and considerably less so when the change of scene consists of a change in the statistical ensemble of surface reflectances in the environment.