Cost effectiveness analysis is increasingly advocated as a basis for health policy. Analysts often compare expensive interventions with highly cost-effective programs such as hypertension screening, implying that if the former were curtailed resources would be reallocated to the latter and the efficiency of health care would improve. However, in practice, savings are unlikely to be targeted in this way. We present refined policy models that take into account actual patterns of resource allocation in the United States, and provide more realistic estimates of the likely uses of savings. We illustrate the implications of these models in an analysis of the effects of diverting funds from an expensive but effective practice. Eliminating such a practice would actually worsen the overall cost-effectiveness of U.S. health care unless there are radical changes in health policy. Cost effectiveness analysis incorrectly predicts health and cost outcomes of policy initiatives because it ignores the political constraints to health care decision-making.