Captive breeding programs aim to maintain populations that are demographically self-sustaining and genetically healthy. It has been well documented that the best way for managed breeding programs to retain gene diversity (GD) and limit inbreeding is to select breeding pairs that minimize a population's average kinship. We used a series of computer simulations to test 4 methods of minimizing average kinship across a variety of scenarios with varying generation lengths, mortality rates, reproductive rates, and rates of breeding pair success. “Static MK Selection” and “Dynamic MK Selection” are 2 methods for iteratively selecting genetically underrepresented individuals for breeding, whereas “Ranked MK Selection” and “Simultaneous MK Selection” are 2 methods for concurrently selecting the group of breeding individuals that produce offspring with the lowest average kinship. For populations with discrete generations (24 tested scenarios), we found that the Simultaneous and Ranked MK Selection methods were generally the best, nearly equivalent methods for selecting breeding pairs that retained GD and limited inbreeding. For populations with overlapping generations (198 tested scenarios), we found that Dynamic MK Selection was the most robust method for selecting breeding pairs. We used these results to provide guidelines for identifying which method of minimizing average kinship was most appropriate for various breeding program scenarios.