The OSV conjecture (2004) states that microstates of four-dimensional supersymmetric black holes are captured by the topological string, by relating the black hole partition function to the topological string partition function. Duality covariance, however, is not manifest in the OSV proposal. We show how the inclusion of a non-trivial integration measure factor restores duality covariance. Our proposal is in agreement with recent results for microstate degeneracies, and it also points to the existence of a consistent non-holomorphic deformation of special geometry.