Predation by introduced foxes and cats is generally thought to be the main reason for the poor success rate of macropod reintroductions on the Australian mainland. Predator-prey theory suggests that predation may have particularly severe impacts on very small populations, especially if a more common primary prey species is present (such as the rabbit). Thus, a sufficiently large reintroduction may overcome predation and succeed where a smaller one would fail. The minimum viable population would, however, be much larger than that predicted by standard population-viability analysis. We use a simple stochastic model based upon the bridled nailtail wallaby to explore this possibility. Even very small amounts of predation (2-4 individuals per six months) can be sufficient to cause reintroductions of up to 50 animals to fail. No clear threshold population size beyond which reintroductions will succeed is evident and, for a given mean, the probability distribution of predation has a very limited impact on the success of reintroductions. In almost all circumstances, a single reintroduction of a given size is preferable to multiple reintroductions of the same total number of individuals.