This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development-such as the reference prior approach-often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain types of structure. To take advantage of structure, this article proposes embedding the original problem in a continuous problem that preserves the structure, and then using standard reference prior theory to determine the appropriate objective prior. Four different possibilities for this embedding are explored, and applied to a population-size model, the hypergeometric distribution, the multivariate hypergeometric distribution, the binomial-beta distribution, and the binomial distribution. The recommended objective priors for the first, third, and fourth problems are new. © 2012 American Statistical Association.