Tree breeders often face the challenge of conserving genetic diversity, while at the same time maximizing response to selection. When selecting advanced-generation breeding populations, the best-performing candidates will quite often be closely related and selecting them without consideration of their relatedness will very quickly erode genetic diversity. Optimal selection will not completely avoid kinship, but rather maximize gain while imposing a constraint on average relatedness. Genetic contributions are most easily optimized if breeders can manage a real, continuous distribution of contributions from parents. While generally possible when establishing seed orchards, unequal contributions to a breeding population may present difficult and time-consuming operational constraints. In these situations, a specified number of parents contributing equally may be a preferred configuration for the breeding population. Here we formulate the selection of a fixed-size breeding population while imposing a constraint on relatedness of the population members. The problem is expressed as a Mixed Integer Quadratically Constrained Optimization (MIQCO) and solved using branch-and-bound techniques (BB). An open-source solver, dsOpt, was developed and embedded into a user-friendly tool, OPSEL, designed to simplify the process of optimizing selection of breeding populations. Case studies optimizing selection of breeding populations for Scots pine and loblolly pine illustrate the superiority of the BB solution compared with selection from ranked lists with restrictions on numbers of genotypes contributed by each full-sib family, and with solutions from GENCONT, a publically available optimum selection program using an algorithm with Lagrangian multipliers. The case studies also illustrate the extreme differences that can occur with respect to time required to confirm the optimality of solutions found by BB.