The optimal hunting mortality rate and proportion of adult males in the harvest are found as functions of the size and structure of the saiga population before hunting. The effects of stochastic climatic variation on the population are taken into account in this model. It is shown that key assumptions must be made about the effects of the breeding sex ratio on female fecundity, and about whether poaching is occurring. If incorrect assumptions are made about either of these factors, the calculated optimal strategy can become severely suboptimal. A simple suboptimal decision rule that takes the population size and structure into account is shown to be more able to buffer against these factors than the optimal strategy, which has proved too complicated for analytical solution. The model predictions are robust to parameter changes.