BACK in the days of Boutros Boutros-Ghali and Javier Pérez de Cuéllar, a British comedian joked that the prime qualification for becoming UN secretary-general was to have a long and hard-to-pronounce name. Since custom dictates that the job rotates between regions and it is now the turn of Eastern Europe, a region with many splendidly difficult names, you might think that the rule would be fulfilled. Perhaps not.

Both of the leading candidates are women from Bulgaria. Both have names that are pronounced more or less as their English transliterations indicate. But the question of which one Bulgaria’s government will nominate is already causing political turbulence at home.

Secretaries-general of the United Nations cannot propose or veto binding legislation, order troops into battle or issue executive orders. But they can sometimes set the agenda or mediate between warring parties. So for small countries that crave a bit of global influence, placing one of their citizens in the UN’s top job is a coveted prize. Ban Ki-Moon’s second term as secretary-general ends in 2017, and the race to succeed him is already under way.

The UN’s boss is selected by the Security Council, which means that Russia and America, both permanent members, have a great deal of sway. Much pressure has been exerted, particularly by America, to pick the UN’s first-ever female head. The race will be dirty: candidates and their allies have been quietly campaigning against one another, and some have promised that evidence of their rivals’ corruption will soon emerge. The campaigners must play two simultaneous games of political chess: domestic, in order to win their governments’ nominations, and international, to curry favour in Washington and Moscow.

The Bulgarians are both strong candidates. One is Irina Bokova, who currently leads UNESCO, the UN’s cultural and educational organisation. Her rival is Kristalina Georgieva (pictured), the European Commission’s vice-president in charge of the budget. Last week Ms Georgieva presented an ambitious new plan for funding humanitarian aid, in her capacity as co-chair of a commission appointed by Mr Ban. The appointment suggested that she is the current secretary-general’s preferred choice.

In Sofia, Boyko Borisov, the prime minister, is under pressure to decide which woman he will nominate. He is close to Ms Georgieva and would prefer to keep her as an ally in Brussels, but he may pick her nevertheless. Ms Bokova, meanwhile, is tied to the political opposition, but one small party in the governing coalition is also on her side. On January 14th its leader threatened to pull out of the government unless Mr Borisov nominated her. Ms Bokova once enjoyed American support, but made enemies by lobbying Washington to accept the accession of the Palestinian Authority as a UNESCO member in 2011. (America ended its contributions to the organisation, which had covered 22% of its budget.) She is now seen as Russia’s preferred candidate.

Every twist and turn in the battle is being followed by a second rank of candidates, each hoping that the Bulgarians will knock each other out. Yet all of the second-tier candidates have problems of their own. Vesna Pusic, the outgoing Croatian foreign minister, has long wanted the job, but the incoming Croatian government is unlikely to nominate her.

The next rung of candidates face the disadvantage that they fail the “testicular test”, as Richard Gowan of the European Council on Foreign Relations puts it. The campaign of Danilo Turk, a former Slovene president, has not excited much interest. Igor Luksic, the Montenegrin foreign minister, has little chance of being picked; his campaign is thought to be a profile-raising exercise for another international job down the line. Srgjan Kerim, a former Macedonian foreign minister, is a no-hoper.

Two candidates who do stand a fair chance if the Bulgarians fail are Vuk Jeremic, a former Serbian foreign minister, and Miroslav Lajcak, the Slovak foreign minister (who has spent much of his career in the Balkans). Mr Jeremic made enemies in many Western capitals by campaigning against international recognition of Kosovo’s independence in 2008. Recently he has been finding influential allies in America to help overcome that legacy, though he still needs to persuade his own government to nominate him. Mr Lajcak is a dark horse. If the current Slovak government is re-elected in March then he will probably be nominated.

If the Russians and Americans cannot agree on any of the names already in the race, then many others now under the radar could “pop up at the very last moment,” says Mr Gowan. Some of them may not even be eastern Europeans. But for now, the Balkan candidates remain the likeliest bet.