Color-appearance models, CIECAM02 and CAM16, usually include two one-step chromatic adaptation transforms: a forward (one-step) transform to convert data from a first illuminant to CIE illuminant E, plus a reverse (one-step) transform to convert the results from CIE illuminant E to a second illuminant. In practice, however, one-step chromatic adaptation models, that avoid the use of the intermediate CIE illuminant E, are also employed. Tests using the one-step CAT16 model indicate failures of both the symmetry and transitivity properties, except in the case where the degree of adaptation D is equal to unity. The magnitude of these failures depends on the specific illuminants selected, and increases as the degree of adaptation decreases. From four possible two-step CAT16 models, we have identified two that obey the symmetry and transitivity properties, one with slightly better predictions of the experimental corresponding-color datasets available in the literature, and more consistent with the one-step CAT16 model. The findings of this article confirm that, for incomplete adaptation, the use of the one-step CAT is incorrect, and we propose that the use of a two-step CAT16 model be mandatory for future applications.