A doctor of economics, Bajuk had held senior positions at the World Bank and the Inter-American Development Bank before shooting to political fame almost overnight in 2000.

Almost unknown outside the Slovenian diaspora in Argentina when he came to Slovenia, he was named prime minister of a short-lived interim government.

He was at the helm of the government from April 2000, when the cabinet of Janez Drnovsek lost a confidence vote in parliament, until the election at the end of 2000, when the centre-left took the reigns once again.

After spending the four intervening years in the opposition, Bajuk was named in 2004 the finance minister in the government of Janez Jansa, serving the full four-year term.

In 2005 The Banker magazine named him the best finance minister in the EU.

While Bajuk made his name as an outspoken MP and his track record in government was widely perceived as successful, he is also credited with having helped strengthen Jansa's Democrats (SDS) at the expense of other centre-right parties.

The Bajuk cabinet was formed in 2000 by the SDS and SLS+SKD, a party created after the Christian Democrats and People's Party joined ranks earlier that year.

Yet infighting soon engulfed the party over changes to the election system and Bajuk split off to form a more conservative and Christian New Slovenia (NSi) just a few months before the general election.

The NSi did surprisingly well in the 2000 election, but the combined result of the NSi and the SLS+SKD still fell well short of what the SLS+SKD achieved four years earlier.

In 2004 the NSi did well and entered a coalition with the SDS, SLS and Pensioners' Party (DeSUS), in what would turn out to be its apex.

Bajuk resigned as the head of the NSi at the end of 2008, after the party failed to make the threshold for parliament. He retired from active politics.