The brushtail possum (Trichosurus vulpecula), introduced to New Zealand in 1858, is a significant conservation pest and a major vector of bovine tuberculosis (Tb; Mycobacterium bovis). Consequently, central and local government agencies now spend more than $30 million (NZD) each year on possum management activities. The current objective of this effort is selective, sustained control to eliminate the transmission of Tb to domestic livestock (which is assumed to require a 60% reduction in possum numbers) and to protect the areas with high ranking indigenous flora and fauna that are most at risk from possums (assumed to require a 80% reduction in numbers). Previous simulation studies have suggested that regular aerial control with bait containing sodium monofluoroacetate (1080) is the most cost-effective large-scale possum control strategy. However, there is a growing awareness that the survivors of 1080 operations can develop ‘bait shyness’. This factor can markedly alter the efficacy of future 1080 control operations but has not been considered in previous simulation studies. I, therefore, constructed a possum control simulation model to assist in identifying the most cost-effective control strategy that would achieve sustained population reductions of 60% and 80%, given bait-shy behaviour and rapid possum population recovery due to immigration. The simulation results suggest that it is possible to achieve sustained 60% or 80% reductions in possum numbers using a 1080-based control strategy, provided reasonably large (>100 ha) areas are controlled and 90% of susceptible possums are killed in the 1080 operations. The chronic-acting toxicant brodifacoum (Talon) will kill the majority of any non-susceptible (i.e., 1080 bait-shy) survivors and its occasional use instead of 1080 during the follow-up control phase provided the most cost-effective way of maintaining a possum population at low density. Sensitivity analysis indicated that the most important variable influencing the overall sucess of these control strategies was the maximum rate of re-colonisation following control. With the high rates of immigration that are sometimes observed in small forest reserves, it was not possible to maintain a sustained 80% reduction in numbers using any combination of toxicants. Expensive, permanent bait stations may be required to minimise the effects of immigration into these small reserves.