We study theoretically and experimentally a game in which players of different abilities self-organize in teams, either homogeneous or heterogeneous. We first consider two standard incentive schemes used in organisations: rewarding the best performing team or the best performing member of each team, both measured with an imperfect benchmarking technology. When used individually, these schemes lead to the efficient matching of purely self-interested players when homogeneous teams maximize total surplus. However, it is not the case when heterogeneous teams do. We then show that there always exists a combination of the two schemes leading to the surplus maximizing matching. We test the theory in the laboratory and find results that are largely consistent with our predictions for self-interested players. However, this is only the case when subjects are provided with sufficient information about their expected payoffs. Despite randomly allocating players to different ability parameters, few high ability subjects seem to perceive this allocation as sufficiently unfair to deviate from their predicted behaviour.