We characterize the optimal structure of prizes in contests, when the contest designer is interested in the maximization of either the expected total effort or the expected highest effort. The all-pay auction framework in the present paper makes it possible to derive most of the results in Moldovanu and Sela's (2001, American Economic Review, 542-558; 2006, Journal of Economic Theory, 70-96) incomplete-information model of contests in a particularly simple fashion, as well as to obtain new results.