Scandals over the manipulation of Libor, foreign exchange benchmarks, and other financial benchmarks have spurred policy discussions over the appropriate design of benchmark fixings. We introduce a framework for the design of a benchmark fixing as an estimator of fair market value. The fixing data are the reports or transactions of agents whose profits depend on the fixing, and who may therefore have incentives to manipulate the fixing. We focus on linear fixings, which are weighted sums of transaction prices, with weights that depend on transaction sizes. We derive the optimal fixing under a simplifying assumption that weights are unidimensional, and we axiomatically characterize the unique benchmark 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 for a variant of VWAP based on unidimensional size weights. We characterize the relative advantages of these fixing designs, depending on the market characteristics.