Wildlife managers often have a good understanding of the threats faced by populations, but they need to know the intensity of management required for populations to survive. Managers therefore need quantitative projections for populations under different management regimes rather than just qualitative comparisons. However, quantitative projections are subject to tremendous uncertainty, particularly for small populations monitored for short time spans. We assess the level of predator control needed for a reintroduced population of North Island robins (Petroica longipes) to grow, accounting for uncertainty associated with parameter estimation, model structure, and demographic stochasticity. The robin population grew when exotic rats were reduced to low levels (<10% of footprint tunnels tracked in 24 hr) by regular maintenance of poison bait stations. However, the population declined after baiting was stopped 3 years after the reintroduction (March 2002), and it had fallen to 4 pairs by September 2004. We created a simulation model incorporating relationships between vital rates (survival and fecundity) of the robin population and rat tracking rate estimated from 5 years of data. We ran the model 10,000 times at each rat tracking rate, with vital rates sampled from distributions (defined by estimates and standard errors) at the start of each run. Output from a deterministic model suggested that λ (finite rate of increase) would be >1 if rat tracking were <20%, and up to 1.2 with rat tracking at 1%. However, 95% confidence intervals for λ extended <1 at any tracking rate. With demographic stochasticity added, there was >20% probability of further decline in 5 years even when the expected λ was 1.2. With all forms of uncertainty included, 41% of simulations projected a further decline over 5 years if the rat tracking rate were 10%. This proportion was reduced to 30% if initial population size was increased to 20 pairs. Our analysis therefore showed it was most likely that the robin population would grow if intensive rat control were reinstated, particularly if the population was supplemented, but there was substantial risk the population would continue to decline under such management.