How to manage harvest under great uncertainty is a fundamental question for many wildlife managers, particularly when resources necessary to estimate abundance or population trends are limited. The large Newfoundland and Labrador murre hunt is the only licensed harvest of seabirds in Canada. Though harvest of thick‐billed murres (Uria lomvia) and common murres (Uria aalge) has declined considerably since the 1960−1970s from >500,000 birds taken annually to approximately 100,000 annually in recent years, potential murre colony declines across the North Atlantic have again triggered concerns over the sustainability of murre harvest in Canada. The effect of current harvest is difficult to assess because there is considerable uncertainty in recent population size, trend, demographic rates, licensed harvest, fisheries bycatch, and illegal harvest. To assess the situation, we simulated the population size necessary to sustain current levels of approximated anthropogenic mortality using a potential biological removal approach, which simplifies and constrains population processes to a few key variables. Based on these simulations, the Canadian licensed harvest of thick‐billed murre is consistent with conservation management objectives, as is common murre licensed harvest and fisheries bycatch. Adding estimated illegal harvest resulted in unstainable mortality levels in both species. While wildlife managers will need to formally assess the relative costs and benefits of reducing uncertainty in this system through improved harvest and population monitoring, illegal harvest and commercialization need to be addressed to manage Canadian murre populations. Potential biological removal approaches can be a useful framework to assess harvest management decisions for marine birds and other data‐limited species.