EVERY winter, northern Europeans bound for ski holidays zip insouciantly through the Netherlands, Belgium and Germany on motorways that are free of charge. But near the borders of Austria or Switzerland they must pull over to buy stickers so that they can drive on the Alpine motorways—even as Austrian and Swiss cars zoom in the opposite direction onto Germany’s free Autobahn. To the perceived injustices in the European Union (EU), add another: the nuisances of a quilt of road-tolls.

Bavarians are particularly cranky. If you live in Munich, say, work and play extend naturally across the border. Hence the grousing about paying on Austrian roads while Austrians “free-ride” on Bavarian ones. In 2013 the CSU, a regional party that governs Bavaria, made fixing “this unfair situation” a condition for joining the coalition of the chancellor, Angela Merkel. The CSU’s Alexander Dobrindt, who became transport minister, got to work.

He knew that his biggest hurdle would be the EU, which forbids discriminating against the citizens of other member states. So he came up with two nominally separate laws. In one, everyone, German or foreign, would be charged a new road toll, like Austria’s. In the other, Germans would get a cut in their vehicle tax that miraculously equals the price of the new toll. In effect, only foreigners would have paid more to use the Autobahn. That was a bit too cheeky for the European Commission, which in 2015 flashed a stop sign in front of Mr Dobrindt. But now he has struck a compromise with Brussels. The proposed toll will be cheaper, and the tax relief for Germans better disguised.

That still has other Europeans fuming about Bavarian harassment aimed at them. Austria and the Netherlands, possibly joined by Denmark and Belgium, may sue Germany before the European Court of Justice. A Bavarian pet peeve has thus escalated to crisis diplomacy. “We in Austria are very unhappy about this,” Christian Kern, the Austrian chancellor, said in December. “This is a stress test for good German-Austrian relations.” Mr Dobrindt retorted: “I have little sympathy for this toll-whingeing, especially when it comes from Austria.” It seems that the EU will always find new ways to puncture its own tyres.