Optimal quality provision is a fundamental concern in regulated health care markets. Some state-funded or regulated programs have implemented payment systems that aim at increasing quality provision by rewarding clinical quality and relying on consumer choice and competition. However, in health care markets, quality is a multidimensional concept. While clinical quality affects health outcomes and has public health externalities, consumer decisions about providers are typically driven by perceptions about general quality or reputation. In this paper, we explore the role of quality multi-dimensionality in public General Practitioner ("GP") services in England. We show how multi-dimensional quality affects not only patients allocation and choices, but also practices quality provision choices. In counterfactual exercises, we compare and quantify the welfare consequences of different payment regimes.