We model the design of a benchmark fixing as an estimator of fair market value. The fixing data are the transactions of agents whose profits depend on the fixing, implying incentives for manipulation. We derive the optimal linear fixing under an assumption that transaction weights are unidimensional. We also axiomatically characterize the unique linear fixing that is robust to a certain form of collusion among traders. Our analysis provides a foundation for the commonly used volume-weighted average price (VWAP) and its analogue based on unidimensional weights. We characterize the relative advantages of these fixing designs, depending on market characteristics.