THE anti-immigrant Danish People’s Party (DPP) has been in the vanguard of Europe’s populist right for a decade and a half. It scored huge gains in elections on June 18th, coming second with 21% of the vote. But the DPP will not be joining the centre-right government announced last week by Lars Lokke Rasmussen of the Liberal Party. Indeed, no other parties will. Unable to form a coalition due to policy divisions, Mr Rasmussen will lead a single-party minority government, with tacit parliamentary backing from the DPP and two other right-leaning parties. Together they have a fragile one-vote majority in Denmark’s 179-seat parliament. And with 37 seats to the Liberals’ 34, the DPP is already starting to show its power.

Mr Rasmussen’s defeat of Helle Thorning-Schmidt’s Social Democrat-led administration was far from definitive. The Social Democrats remain the largest party in parliament with 47 seats. While no left-leaning coalition was possible, the so-called “blue bloc” is deeply split too. The Liberals and the DPP disagree on taxes, social spending and the European Union, leading the DPP to turn down Mr Rasmussen’s offer of cabinet seats.

Denmark’s multiparty political system frequently produces minority governments, but this one seems unusually tricky. The surge in support for the DPP has it brimming with confidence and determined to drive hard bargains. While Mr Rasmussen was still trying to form a coalition last week, an EU summit required the attendance of Ms Thorning-Schmidt as caretaker prime minister. Mr Rasmussen gave her his blessing. But the DPP’s Eurosceptic leader, Kristian Thulesen Dahl, warned her to keep a low profile and caustically remarked that she would enjoy a last meeting with her Brussels friends.

While Mr Thulesen Dahl’s refusal to enter a coalition disappointed many of his voters, the DPP is well-versed in exercising power from the sidelines. From 2001-2011 it bartered its parliamentary weight for concessions on social spending and tighter immigration rules.

To counterbalance the DPP’s power, Mr Rasmussen has promised to “work broadly in parliament”, the Danish euphemism for cobbling together support on a case-by-case basis. One of his first acts was to reintroduce a tax break for home improvements, an idea backed by two small leftist parties but opposed by the Liberal Alliance, a putative ally. Yet he also dispatched his foreign minister to Berlin to explain Denmark’s plans for beefing up border security. This is a central plank of the DPP’s platform, and may violate Europe’s Schengen open-border rules.

By making both moves in his first week in office Mr Rasmussen showed his willingness to cross ideological divides. But piecemeal governance is hard, even in consensus-driven Denmark. Just one defector on the right could topple him.