We explored limits and consequences of male-biased harvesting of polar bears Ursus maritimus using a simulated population based on empirically-derived estimates of age-specific rates of survival and reproduction. The maximum sustainable yield (MSY) was identified as the total kill in which the number of females that could be taken resulted in ≤5% change in females older than 50 years. MSY depended on the proportion of males in the harvest, although the effect of male selection on the post-harvest population was to reduce the mean age and number of males. A practical limit to the increase in MSY possible from male-selective harvesting was identified at the 3 : 1 (M/F) sex ratio. At 3 : 1 (M/F), all males were eventually harvested as 2-year olds, and males were reduced to 25% of pre-harvest levels. A more conservative harvest strategy of 2 : 1 (M/F) resulted in a 30% reduction of males and a reduction of the mean age of males from 10.0 to 7.7 years post-harvest. We thus recommend that sex-selective harvesting of polar bears do not exceed 67% males (i.e. a harvest ratio of 2 : 1), a demonstrably safe and sustainable harvest strategy, to avoid depletion of males and possibly reduce recruitment by having too few sexually mature males in the population. When females are harvested below MSY, then harvest strategies that select for males at rates > 2 : 1 (M/F) can be conservative because the increase in females also increases the reproductive performance of the population. In the absence of information on density effects, managers should be conservative in their expectations of increases in the female population.