The inspirational story is Brazil, where a $30bn IMF package in 2002 allied to a plan for fiscal stringency helped restore confidence in the government's debt.
The cautionary tale is Argentina, where the fund extended loans to a country that could not stick to the tax and spending targets it agreed, and which in 2001 succumbed to the largest sovereign default in history.
The difficult balance is to achieve a fiscal tightening that will reassure the capital markets and reduce the risk premium on Greek debt without plunging the country into such a deep recession there is too little revenue to service the debt.
"The key is not the short-term financing but taking actions in the short-term that give confidence about medium-term fiscal sustainability," said Ousmène Mandeng, head of public sector investment advice at Ashmore Investment Management and a former IMF official. "The programme needs to be front-loaded, because it needs to show that the country is capable of taking the pain."
Calculations rest on such fickle variables as the appetite for risk among investors and market confidence in the government.
Simon Johnson, a former IMF chief economist, said the rescue had little chance of working. "The clear comparison with Argentina is the fixed exchange rate." Greece is stuck in the eurozone: Argentina fixed its peso to the dollar. "This looks exactly like the traditional problem of an emerging market with an overvalued fixed exchange rate."
During the crisis, he said, the ratio of Argentina's debt to gross domestic product was 62 per cent, with Greece's almost twice as high. The Argentinian fiscal deficit reached 6.4 per cent of GDP, compared with Greece's 12.7 per cent.
Mr Johnson calculates that Greece would need a rescue package of about €200bn ($270bn, £176bn) over the next three years. But with the likelihood of a much smaller loan of €40bn to €45bn, the country will have to swing from last year's primary deficit of 7.7 per cent to a primary deficit of about 6 per cent in a couple of years - a huge tightening of fiscal policy that will require savage cuts in public wages and services.
IMF officials note that some countries have pulled off similar shifts - Jamaica in the late 1970s and early 1980s being one - but few within such a short time-frame. Such a task seems improbable in a country where even relatively modest moves to hold down spending and wages have provoked unrest.
The alternative is for Greece to restructure its debt before the market pushes it into default. But that would involve forcing holders of Greek debt - believed to include German and French banks - to take losses, which could affect their capital requirements and is likely to be resisted by the eurozone governments co-financing the deal.
Hope burns brightly in the fund that this could be another Brazil: fear that it could be a re-run of Argentina casts a long shadow. * European Union and IMF officials have postponed today's meeting on an emergency bail-out package for Greece after flights to Athens were cancelled because of volcanic ash, writes Kerin Hope in Athens .