School accountability schemes require measures of school performance, and these measures are in practice often based on pupil test scores. It is well-known that insufficiently correcting these test scores for pupil characteristics may provide incentives for inefficient pupil selection. We show that the trade-off between reward and pupil selection is not only a matter of sufficient information. A school accountability scheme that rewards school performance will create incentives for pupil selection, even under perfect information, unless the educational production function satisfies an (unrealistic) separability assumption. We propose different compromise solutions and discuss the resulting incentives in theory. The empirical relevance of our analysis – i.e., the rejection of the separability assumption and the magnitude of the incentives in the different compromise solutions – is illustrated with Flemish data.