The brushtail possum is a significant conservation pest and major vector of bovine tuberculosis in New Zealand. Previous control simulation studies have suggested that 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 control can develop ‘bait shyness’, and this can markedly alter the efficacy of ongoing 1080 control operations. Several alternative toxicants are registered for possum control but all are ground based, differ in their mode of action, and are more expensive than aerial 1080 control. A new possum control simulation model was developed to assist in identifying the most cost-effective control strategy that would achieve a sustained 80% population reduction, given bait-shy behaviour and immigration from adjacent non-controlled areas. The simulation results indicated that it is possible to achieve a sustained 80% population reduction (over a 10-year period) using a 1080-based control strategy, provided at least 90% of all ‘susceptible’ possums are killed in each control operation. In the event of an unsuccessful 1080 control operation (i.e., only a 60% kill), cyanide bait plus trapping, or brodifacoum bait provided the most cost-effective strategy of ‘mopping up’ 1080 bait-shy survivors. However, sufficient numbers of traps must accompany the cyanide bait to ensure that the majority of 1080 bait-shy possums are targeted. Sensitivity analysis indicated that the most important variable influencing the overall success of any control strategies was the rate of re-colonization following control. With the high rates of immigration that are sometimes observed in small forest reserves (i.e., <100 ha), it was not possible to sustain an 80% population reduction using any combination of toxicants. However, higher rates of immigration are probably exceptional and the rate used in these simulations is considered more typical, particularly for moderate-to-large forest stands where most possum control is conducted.