Linking age-specific vital rates to population growth through demographic matrix models can enhance our understanding of crucial population processes, vital in a conservation context. The white-tailed eagle (Haliaeetus albicilla) population in the Federal State of Schleswig-Holstein, Germany, has been monitored since re-colonisation in 1947 and provides a well-documented example of a recovery. We test how demographic models capture growth trajectories of a recovering population and how applicable they are in guiding population management of endangered species. From 1947 to 1974, the population was stable but the growth rate predicted by an age-structured matrix model was −6.1% per annum. The small but stable population must have been maintained by immigration. From 1975 to 2008, observed and predicted population growths were very similar (6.7% and 4% per annum respectively). Elasticity and life-stage simulation analyses identified adult and pre-breeding survival as key vital rate elements. While the prospective analyses identified survival as the key vital rate influencing population growth, the increasing reproduction rate allowed the recovery to take place; thus caution is needed when prospective modelling makes management recommendations. Nevertheless, conservation efforts should address key mortality factors such as lead poisoning and collision with wind turbines. A logistic model predicted a maximum carrying capacity of 255 pairs for the Federal State, but using the highest currently observed density (1.4 pairs per 100 km2) and differences in habitat suitability, a more likely carrying capacity was estimated at 122 pairs. Under both scenarios, current population growth should slow soon.