REVERBERATIONS from Britain’s vote to leave the European Union have travelled from the Thames to the Tiber. Italian banks’ shares have plunged: Monte dei Paschi di Siena, the third-biggest (and the world’s oldest), has lost half its value since the Brexit vote. This has prompted Matteo Renzi, the prime minister, to propose recapitalising the weakest banks with public money. But there is a snag: many Italian savers own bank bonds, which under EU rules stand to be written off if lenders receive state aid. Can Mr Renzi save both the banks and the bondholders—and his job? Italian banks are labouring under Europe’s biggest bad-loan burden: €360m ($400m), or 18% of the total, the product of years of economic stagnation and questionable lending. Several other countries, including Britain and Germany, spent oodles bailing out banks after the crisis of 2008. Italy, facing less acute problems, did not. The bad loans meanwhile piled up: writing them down further or selling them will eat capital, which needs replenishment. The EU rules—tightened in the past three years—say that additional capital should come from the private sector. Although some banks can turn to the markets, others are too weak. A fund set up recently by the financial industry to recapitalise frail lenders and buy bad loans has already used much of its money.

Mr Renzi wants to protect bondholders at all costs. When investors were soaked after the rescue of four tiny banks last November, uproar ensued—and a man killed himself. A repeat may seal the prime minister’s defeat in a referendum in October on constitutional reform, on which he has staked his premiership. For the European Commission, which oversees state aid, the stakes are also high. This is the first test of its tighter rules, and if they are bent out of shape to suit Mr Renzi they will no longer be credible.

Officials from Italy and the commission are trying to find a way of permitting a bail-out without either breaking the rules or bashing the bondholders—perhaps involving "precautionary” recapitalisation. The results of “stress tests” of European banks, due on July 29th, which may show up weaknesses at Monte dei Paschi and elsewhere, add urgency. It is in both sides’ interest to use whatever wriggle room there is. So soon after the Brexit vote, the EU can ill afford a bust-up between Brussels and a founding member state.