Two potentially asymmetric players compete for a prize of common value, which is initially unknown, by exerting effort. A designer has two instruments for contest design. First, she decides whether and how to disclose an informative signal of the prize value to players. Second, she sets the scoring rule for the contest, which can be biased in favor of one player. We show that the optimum depends on the designer's objective. An ex post symmetric contest in which information is symmetrically distributed and the scoring rule offsets the initial asymmetry between players always maximizes the expected total effort. However, the optimal contest may create dual asymmetry i.e., the designer discloses the signal privately to one player, while favoring the other in terms of the scoring rule when the designer is concerned about the expected winner's effort or the expected maximum effort. This could arise even if the players are ex ante symmetric. Our results are qualitatively robust to an endogenous information structure.