Danes are voting in a general election which opinion polls suggest is on a knife edge.
The centre-left coalition of PM Helle Thorning-Schmidt, and the centre-right opposition led by ex-PM Lars Lokke Rasmussen, appear to be neck and neck.
But the pollsters have only canvassed the Danish mainland – and voters in Greenland and the Faroe Islands may decide the vote.
Minor issues like a Faroes fishing dispute could influence the result.
The islands’ fishing community is still angry at Ms Thorning-Schmidt for barring its boats from Danish ports in a 2013 dispute over alleged overfishing.
But in reality it is the economy, rather than mackerel quotas, that tends to swing elections, and Ms Thorning-Schmidt’s Social Democrat party has staged a remarkable comeback in recent weeks as Danish finances improve.
Welfare and immigration are exercising Danish voters even more than the economy, with anger at perceived benefit tourism leading the traditionally pro-immigration Social Democrats to launch an advertising campaign with the slogan: “If you come to Denmark you should work.”
Mr Rasmussen, who led the country between 2009 and 2011, has suggested that benefits are so high that there is barely any incentive for Danes or immigrants to work.
Hours before the polls opened, party leaders took part in the final debate on Danish TV.
A poll released on Tuesday put the centre-left bloc – the Social Democrats and their four coalition partners – on 50.1% and the centre-right bloc led by Mr Rasmussen on 49.9%.
Either one of Ms Thorning-Schmidt’s and Mr Rasmussen’s parties could win the most seats, only to find themselves the loser if the other can muster a larger coalition.