Populations established with a small number of founders are thought to have a high risk of extinction due to allee effects, demographic stochasticity, inbreeding and reduced genetic variation. We tested whether the initial number of birds released was related to persistence in reintroductions of saddlebacks (Philesturnus carunculatus) and robins (Petroica australis) to New Zealand offshore islands. Data were analysed for 31 populations that had been observed for at least 3 years since reintroductions. The numbers released ranged from 5–188. Most of the populations (26) survived and grew, including five from less than 15 founders, and four out of the five extinctions were attributable to introduced mammalian predators. The number of individuals released did not significantly affect extinction probability. The ability of these small releases to establish populations can be attributed to the closed nature of the islands (allowing birds to find mates), low mortality rates following release and high growth rates at low density. Stochastic simulation models based on data from two reintroduced populations suggested that populations with four founders (two male, two female) would have a negligible chance of extinction through demographic stochasticity and would be able to grow even if there were high rates of egg failure through inbreeding.