The stoat (Mustela erminea) is a specialist predator that evolved to exploit the unstable populations of northern voles and lemmings. It was introduced to New Zealand, where it is pre-adapted to respond with a population irruption to the resource pulses that follow a heavy seedfall of southern beech (Nothofagus spp.). Culling stoats during an irruption is necessary to reduce damaging predation on nesting endemic birds. Culling might not reduce the stoat population long term, however, if high natural mortality exceeds culling mortality in peak years. During other phases of the beech-mast cycle, culling might have a greater effect on a smaller stoat population, whether or not damage prevention is critical. We developed a 4-matrix model to predict the effects of culling on k, the annual rate of change in the size of the stoat population, through the four annual phases of an average masting cycle, explicitly distinguishing between apparent and real culling. In the Post-seedfall phase of the cycle, large numbers of stoats are killed, but little of this extra mortality is additive; in other phases, culling removes larger proportions of smaller total numbers of stoats that would otherwise have lived. Culling throughout all phases is most effective at reducing stoat populations, but is also the most expensive option. Culling in Postseedfall plus Seed or Crash years is somewhat less effective but better than culling in one phase only. Culling has different short-term effects on stoat age distribution depending on the phase of the cycle when culling begins.