We introduce a class of exchangeable random partition models that allow direct specification of prior beliefs about both the number of clusters and the distribution of cluster sizes. In contrast to random partitions induced by Bayesian nonparametric priors---such as the Dirichlet-process Chinese restaurant process and its Pitman-Yor generalization, where a small number of global parameters jointly determine both the number of clusters and the size distribution---our framework places an explicit prior on the number of clusters and a separate prior on the cluster-size profile. We use Lorenz curves and introduce a family of distributions on integer partitions that accommodate exponential- or power-law tails. Conditional on an integer partition, we place a uniform distribution over all set partitions consistent with it, preserving exchangeability and separating prior elicitation from label combinatorics. This yields exchangeable priors in which the number of clusters and the size profile are specified separately. We treat n as fixed and do not require sampling consistency across n. Computation reduces to repeated evaluation and sampling from bounded-support univariate pmfs with closed-form normalizing constants.