BY NOW Brazil’s president, Dilma Rousseff, must be finding the script wearily familiar. First come the corruption allegations, then the indignant denials, more evidence, equivocation and retractions—and finally another of her ministers has to walk. Since June Ms Rousseff has lost her chief of staff and the ministers of transport, agriculture, tourism and sport, variously accused of influence-peddling, bribe-taking, signing fraudulent deals with shell companies and diverting public funds into party coffers or their own pockets. Now Carlos Lupi, the labour minister, has become the latest to look as if he is heading for the exit.

He is accused of presiding over a department that charged kickbacks for government contracts, of personally accepting free flights from one of those contractors and of siphoning off public money to semi-phantom non-governmental organisations (NGOs). Mr Lupi’s response was pugnacious. He did not know the man in question and had never flown with him, he said. The only way to get him out of his ministry, Mr Lupi added, would be to shoot him (“and it would have to be a big bullet, because I’m a big guy”). Then came photographs of him with both businessman and plane. His defenestration seems to be a matter of time. Barring new revelations, he may go in a wider cabinet shuffle expected early in the new year.

The faxina (“housecleaning”), as Ms Rousseff’s removal of allegedly light-fingered ministers has come to be known, is popular. The latest opinion polls put her and her government’s approval ratings at record highs. But it merely scratches the surface of a problem with roots in the way that politics has developed in Brazil. All presidents since democracy was restored in 1985 have had to form variegated coalitions to obtain legislative majorities. But, complained Fernando Henrique Cardoso, a former president, earlier this month, a “system” has now developed under which parties demand ministries in return for their votes, and then use the public funds they thus gain control of to expand their membership.

The 513 seats in the lower house of Congress are now divided between 23 parties. Ms Rousseff’s governing coalition comprises ten of them, commanding 360 seats (an 11th, with 40 legislators, left after the transport minister was sacked). Several of its smaller members have no discernible aim other than to grow fat on public money. The biggest, the Party of the Brazilian Democratic Movement, an alliance of regional power brokers, switched to join her predecessor, Luiz Inácio Lula da Silva, after he won in 2002 and will stay only as long as it suits. “We have a strong president who is unable to do anything without support in Congress,” says Sylvio Costa of Congresso em Foco, an anti-corruption watchdog. “And that support must be bought.”

When the solution found by Lula’s party managers in his first term—paying parliamentarians for their votes—came to light, the resulting outrage nearly brought him down. With cash ruled out, ministries and other grace-and-favour appointments were left as the main political currency. That led to ministerial inflation: Lula’s cabinet grew from 26 in 2003 to 37 when he stepped down last year. Some parties seem to have run “their” ministries for profit. The Communist Party, for example, has held the sports ministry since Lula took office. Under Orlando Silva, forced out shortly before Mr Lupi’s travails began, it is alleged to have demanded kickbacks on some contracts and funnelled money to affiliates through fake NGOs.