Control of introduced predators is essential for the persistence of many reintroduced species. However, species range in vulnerability from tolerant to completely intolerant, with different tolerances to different predators. Therefore, a prerequisite for efficient conservation management is estimating the tolerances of a range of reintroduced species to introduced predators. We quantified population responses of reintroduced toutouwai (Petroica longipes), popokatea (Mohoua albicilla) and tīeke (Philesturnus rufusater) to increased numbers of two key predators, stoats (Mustela erminea) and cats (Felis catus), at a fenced sanctuary in Aotearoa New Zealand. There were fewer than 0.5 annual detections for these predator species from 2004–2016, but stoat detections increased >10-fold from 2017–2019 and cat detections >30-fold from 2020–2021. We therefore used integrated population models and a dynamic logistic model to estimate the growth and persistence of each bird population pre- and post-2017. We used these models to derive λmax, the finite rate of increase at zero density, which must be >1 for population persistence. The popokatea population showed no sign of having been impacted by the increased predators. The toutouwai population showed tentative decreases in survival and reproduction. Tīeke showed a dramatic reduction in survival and recruitment from 2017–2019 with the population dropping from c. 350 to c. 100. These results show that popokatea are completely tolerant of these stoat and cat levels, but it is unclear whether toutouwai could persist, unclear whether tīeke could persist with the cats, and unlikely they could persist even with small numbers of stoats.