Immigration is often thought of as a measure suited to mitigate the fiscal consequences of demographic ageing for unfunded public pension schemes. Building on Sinn (1997), the paper explores in some more detail the conditions under which immigrants are a net fiscal asset for national pension budgets not only on a temporary basis – i.e., as long as they are paying contributions and before they start drawing benefits – but also in the long run. Illustrative simulations are provided for the cases of Germany, Italy, the UK, and the US. It turns out that the value of immigrants depends on the nature of the pension scheme (Bismarck vs Beveridge). Also, it is strongly affected by the immigrants' characteristics in terms of skills and fertility. Furthermore, effects differ substantially for the cases of temporary vs permanent migration.