Data on acculturation and ethnic-minority health indicate that acculturation has opposite effects on the same health behavior among different ethnic groups; opposite effects on different health behaviors within an ethnic group; opposite effects on the same health behavior for the women vs. the men of most ethnic groups; and no effect whatsoever on some health behaviors for some ethnic groups. This evidence is so incoherent that it is unintelligible, and hence it continues to be largely useless to health psychology and behavioral medicine. This paper presents a new theory of acculturation that renders these confusing data coherent by predicting such changes in minority health behavior a priori. By so doing, the operant model of acculturation has the potential to improve health promotion and disease prevention and thereby reduce ethnic health disparities.