As the European financial crisis continues to percolate, by now a few irreducible facts are distressingly clear:

First, Greece has no hope of repaying its debts as they are now constituted. Thus, the much-contested 110 billion euro bailout plan and the wider subsequent trillion-dollar bailout proferred by the Eurozone countries and the IMF are doomed to fail for the simple reason that they offer only more lending to countries already drowning in debt. Greece has a primary deficit (meaning one that would persist for a number of years unless the country experiences spectacular economic growth) exceeding 6% of GDP and a budget deficit due to financing of the accumulated debt of at least another 4%, in addition to which it faces a GDP contraction for at least three years. Simple math shows that to have a stable debt/GDP ratio Greece must generate a budget surplus of at least 10%, which is basically impossible. A rising debt/GDP ratio together with contracting economy will make financing from private investors very doubtful.

Second, although Greece can default on most of its public debt with a unilateral act of parliament—and the political and economic realities to do this may yet prove irresistible—it would be much better for Greece, the IMF and the rest of the Eurozone if it avoided this. For Greece to give up and default in this way would mean not just horrific economic pain for its citizens but the threat of financial turmoil across Europe and possibly the world, since many major banks are implicated. In addition, the debt of Spain, Portugal, Ireland and possibly Italy and even the United Kingdom would be severely compromised. These governments at the very least would face much higher borrowing costs, making their defaults that much more likely. Since investors know this, there might also be bank runs.

So what is to be done? Greece cannot default, but it can “restructure.” To contrarians this may resemble a default, but many people are capable of maintaining the distinction when it is in their interest to do so, as was the case with New York City in the 1970s. Basically, Greece needs more favorable credit terms—lower interest and longer to pay. The balance sheets of European and other banks holding the restructured Greek bonds to maturity will not be impaired absent mark-to-market accounting, which may be on its way out just in time. In this way, the banks can preserve the useful fiction that they are solvent, until they become so with the help of cheap money from the European Central Bank. Many of Greece’s current bondholders may not agree to this plan but the risk of default would be much, much lower with the restructured rather than the original bonds.

Any such restructuring must be done in conjunction with the IMF and EU so that Greece doesn’t become a financial pariah—or rather, so that Greece can cease to be one. The impact of such a plan would be large; Carl Weinberg of High Frequency Economics figures that restructuring the Greek bonds that mature between now and 2019 into a single self-amortizing 25-year bond at 4.5% would save the country more than 140 billion euros over the next five and a half years. The improvement in servicing the country’s debt together with the ongoing rebalancing of its public finances will revise its credit profile and enable access to loans from private markets.

Does all this sound far-fetched? It shouldn’t. All parties have good reason to work together on it, since there is no palatable alternative. Besides, such a restructuring has succeeded elsewhere, including New York City.