“They need someone with a name that’s known beyond Europe,” said Janwillem Acket, chief economist at Julius Baer in Zurich.

Here are the main candidates being floated as Europe’s possible picks, according to discussions with officials around the continent.

Jeroen Dijsselbloem

The former Dutch finance minister and head of the Eurogroup, the euro area’s powerful team of finance chiefs, earned the respect of colleagues during the region’s crisis overseeing tough negotiations with Greece and establishing the zone’s banking union. Fellow ministers considered him a skilled moderator who could help strike tough compromises.

Cons: Dijsselbloem, 53, has German support and is regarded well by other northern countries, but his candidacy faces pushback from Italy and other southern European members who associate him with the tough austerity imposed on some countries during the region’s debt crisis. He further drew ire over remarks linking the turmoil to southern European spending on “women and drinks.”

Mario Centeno

The Portuguese finance minister and current Eurogroup president, 52, is one of the euro-area’s most senior policy makers. Appointing a national from a country bailed out less than a decade ago would be symbolic, turning the page from a painful chapter in southern Europe’s history.

Cons: The Portuguese already hold the presidency of the United Nations, so another high-profile post would be a tough feat for a small nation. Several officials also compare Centeno’s performance unfavorably with his predecessor.

Kristalina Georgieva

The Bulgarian chief executive officer of the World Bank and former vice president of the European Commission is well qualified as a trained economist with prior leadership positions at international institutions. Her appointment would help fix Eastern Europe’s poor representation in such posts.

Cons: At 65, Georgieva is past the age limit for an IMF managing director, so would need a change in its bylaws to succeed. Unlike Lagarde, Georgieva never served as a finance minister, and European finance chiefs may prefer one of their own.

Mark Carney

The Bank of England governor, 54,  has a particularly impressive resume, having led central banks in both the U.K. and Canada, and having helped to set regulations for global finance.

Cons: a Canadian by birth, Carney holds British and Irish passports, so his selection would technically preserve the hold of Europe on the IMF. But several officials say he’s “not European enough,” and it’s unclear which government would even nominate him.

Olli Rehn

The Bank of Finland governor previously an economy minister and European Union commissioner for economic and monetary affairs, has held several posts that make his resume a strong one. He recently lost out to Lagarde for the ECB role.

Cons: Rehn, 57, managed the bloc’s tough bailouts during the early days of the euro-area crisis while serving as the EU’s economics chief, leaving some countries with bitter memories.

Alexander Stubb

Having served as Finland’s prime minister, and in ministerial roles covering finance, trade and foreign affairs, Stubb has strong credentials. Currently a vice president at the European Investment Bank, he speaks five languages and is considered a charismatic communicator.

Cons: Stubb, 51, was seen as one of the more hawkish politicians during the euro-area crisis and his pick could face opposition from southern Europe.

Nadia Calvino

Spain’s finance minister, 50, is a Socialist woman from Europe’s south, ticking a lot of boxes at a time when center-right politicians in the region have clinched major roles, while leadership positions in global economic policy remain dominated by men. Calvino has prior international experience, having worked as a top official at the European Commission.

Cons: Spain’s caretaker government already won a senior EU job when Josep Borrell Fontelles clinched his role as foreign policy chief — in the compromise where Lagarde got the ECB and Germany’s Ursula von der Leyen was appointed European Commission president.

Bruno Le Maire

French finance minister, 50, denies seeking the job, and would need to step back from his role overseeing the search for Lagarde’s successor if he changed his mind. But he has built an international reputation through his efforts to introduce taxation for tech giants, and within the EU as an advocate to strengthen the euro area.

Cons: Five IMF chiefs have been French, including Lagarde, making the prospect of a sixth ambitious. Also, with Lagarde heading to the ECB, France would be pushing it to appoint another of its own to the helm of a major economic institution.

Wildcard

With no consensus yet, officials say a wildcard candidate, such as a top economist outside the obvious sphere of EU policy making, shouldn’t be excluded.

–With assistance from William Horobin and Joao Lima.