Reform proposals of health care systems in several countries have advocated variations of a risk adjustment/capitation system. These proposals face a serious objection: incentives to risk selection are prevalent in the system. By now, considerable literature has been devoted to finding ways of mitigating, if not eliminating, this problem, while at the same time preserving incentives to efficiency. We contribute to this debate presenting a transfer system that, under some circumstances, attains both provider efficiency and no risk selection. The transfer system extends typical linear payment systems. It can be interpreted as a fixed transfer in the beginning of the period plus an ex-post fund at the end of the period. The novelty rests in the way contributions to this fund are defined.