Following a conceptual analysis of the term "quasi-market", this article will look at four national efforts to reform health-care management in what can be regarded, in respect of the degree of solidarity and universality applied, as three different health-care models. The changes in Chile are a continuation of the country's previous reform, which went further than any other in the region in undermining the solidarity and universality of the health-care model. The conclusion is that it would be beneficial to consolidate purely managerial aspects so that progress can be made with the use of administered prices, relevant information on the quality and cost of care can be produced, and efficiency and effectiveness criteria can be applied to clinical services. In Argentina and Colombia, while there are large differences between the two, the changes that have been made are part of a reform process aimed at encouraging competition while upholding the principles of solidarity and universality. Because change has mainly centred on the financing model, management has had a subordinate place since the outset. In the case of Colombia, the article highlights the excessive complexities of hospital financing, which have combined with regulatory shortcomings to inhibit management change. In the case of Argentina, where hospitals are excessively large, it describes the wide range of hospital management reforms that have resulted from past decentralization, the degree to which management is independent of fiscal discipline and the different ideas that exist of the part played by hospitals in referral systems. In the case of Costa Rica, where health care is primarily public and based on principles of solidarity and universality, the article looks at the creation of internal health markets that resulted from the introduction of a new performance-related organizational and financing model in the Costa Rican Social Security Fund; it notes that the management contracts used have interesting features as regards organization and information and the shaping of a health-care system, but that they are excessively complex and involve high transaction costs, and it analyses the difficulties involved in introducing real provider decentralization and creating performance incentives.