Management of Canada geese (Branta canadensis) can be a balance between providing sustained harvest opportunity while not allowing populations to become overabundant and cause damage. In this paper, we focus on the Atlantic population of Canada geese and use stochastic dynamic programming to determine the optimal harvest strategy over a range of plausible models for population dynamics. There is evidence to suggest that the population exhibits significant age structure, and it is possible to reconstruct age structure from surveys. Consequently the harvest strategy is a function of the age composition, as well as the abundance, of the population. The objective is to maximize harvest while maintaining the number of breeding adults in the population between specified upper and lower limits. In addition, the total harvest capacity is limited and there is uncertainty about the strength of density-dependence. We find that under a density-independent model, harvest is maximized by maintaining the breeding population at the highest acceptable abundance. However if harvest capacity is limited, then the optimal long-term breeding population size is lower than the highest acceptable level, to reduce the risk of the population growing to an unacceptably large size. Under the proposed density-dependent model, harvest is maximized by maintaining the breeding population at an intermediate level between the bounds on acceptable population size; limits to harvest capacity have little effect on the optimal long-term population size. It is clear that the strength of density-dependence and constraints on harvest significantly affect the optimal harvest strategy for this population. Model discrimination might be achieved in the long term, while continuing to meet management goals, by adopting an adaptive management strategy.