All over Europe, ageing populations threaten nations' financial sustainability. In this paper we examine the potential of immigration to strengthen financial sustainability. We look at a particularly challenging case, namely that of Denmark, which has extensive tax-financed welfare programmes that provide a high social safety net. The analysis is based on a forecast for the entire Danish economy made using a dynamic computable general equilibrium model with overlapping generations. Net contributions to the public purse are presented both as cross-sectional figures for a long time horizon and as average individual life-cycle contributions. The main conclusion is that immigrants from richer countries have a positive fiscal impact, while immigrants from poorer countries have a large negative one. The negative effect is caused by both a weak labour market performance and early retirement in combination with the universal Danish welfare schemes.