FRANKFURT, Germany — With their late-night deal to cut Greece's debt and support other wobbly countries, European leaders bought time to work out more lasting solutions to the crisis plaguing the euro currency bloc.

How much time the markets will give them will depend, in part, on their speed and skill in filling in financial complexities of the debt swap and bond insurance plan they outlined.

Along with that, countries with sluggish economies, particularly Italy, will have to show that they are becoming better places to do business and improving growth — the key to paying down debt in the long run.

So the debt crisis is still far from over. But with luck the eurozone's 17 governments just might get a chance to work on it for a while without fear that a single misstep will take the shared currency over the edge.

That respite could be short, however, if they return to the fudges and procrastination that have marked their response to the crisis, which broke out two years and six days ago, on Oct. 21, 2009. That's when Greece admitted to the EU statistics agency that its finances were much worse than reported.

Since then, more than a dozen late-night summits and carefully negotiated and crafted statements have failed to get ahead of market fears that Greece would default on its debts and sink the banking system and the wider economy. The crisis also took down Ireland and Portugal, which like Greece were forced to take a bailout because they couldn't borrow affordably and faced default on maturing bonds.

Thursday's deal at long last appears to have met or beaten expectations for some kind of decisive action.

"The summit is likely to be the corner from where the odds start to change in the right direction," said Erik Nielsen, global chief economist at Unicredit.

The most difficult part of the plan was persuading banks to take 50 percent losses on their Greek bonds to help shrink the country's debt pile to where it can be repaid. European leaders then agreed to push Europe's banks to raise (euro) 106 billion in new capital by June, to protect against losses from the Greek debt writedown. The money will come from governments if it can't be raised from investors or by selling assets.

Critically, the debt deal also beefed up the eurozone's underpowered bailout fund so it can convincingly prop up the bonds of bigger countries such as Italy. Supporting the bond prices will keep the countries' borrowing costs from rising, which is what sank smaller Greece, Ireland and Portugal.

The hope now is that the trio of measures will give European countries some breathing space within which to focus on getting their economies growing again. That would help reduce debt and boost confidence in the region's financial markets and banking sectors, reversing what had threatened to be a downward spiral.

It is clear, however, that such a virtuous cycle of events will prove difficult to get going.

To begin with, there are doubts on how the leverage of the eurozone bailout fund's limited resources will work. The European Financial Stability Facility would guarantee part of the value of bonds issued by countries such as Italy and Spain. The idea is to relieve fears of default and lower the interest rate investors want to help the countries roll over their debts.

Joerg Kraemer, the chief economist at Commerzbank, said it was not at all clear that such a guarantee — which essentially admits there are fears of default — will appeal to government bond investors, who typically want safe investments.

And the "voluntary" Greek writedown pushed on banks might convince some potential bond buyers that if there's more trouble, they'll be asked to pony up instead of being compensated through the insurance program.

If the insurance isn't enough to magnify the EFSF's power, governments may face having to kick in more financing for the EFSF. With publics annoyed at bailouts, governments will resist unless the fate of the euro appears once again at stake — meaning back to the brink.

"This alone suggests that the sovereign debt crisis will continue to become exacerbated before ebbing off," said Kraemer.

Europe's finachial crisis Q&A

Here are some questions and answers about what happened and what it means.

Q: What was the original problem?

A: The Greek government spent too much, didn't collect enough in taxes and had to sell bonds to make up the difference. It ran up budget deficits well beyond limits set by the European Union, a group of 27 nations that allow goods and workers to cross their borders freely.

When Greece fell into recession two years ago, bondholders worried they wouldn't get their money back. To make sure they did, the EU started lending money to Greece, essentially allowing it to use new debt to pay off old debt.

Greece shares a currency, the euro, with 16 countries, so its problems are Italy's problems, and Spain's, and Germany's, too. And many other European countries have debt problems of their own.

The challenge was to figure out a way to fix the problem so Greece didn't have to come back for bailout after bailout.

Q: Is the risk from Europe gone?

A: No. Even if the rescue package keeps Greece and the European banks afloat, the crisis has already damaged the European economy. Some manufacturers have slashed production and hoarded cash. Banks are demanding higher rates for loans, if they're lending at all.

On Monday, an important economic indicator suggested business activity in the zone of nations that use the euro currency shrank in October for the first time in three years.

The European Union accounts for 20 percent of world's economic output. It is a big trading partner for many countries. A recession there could push other economies into recession.

Q: How vulnerable is the U.S.?

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Some good news out Thursday suggests the U.S. is in better shape to weather any blow. The economy grew almost twice as fast over the summer as it did in the spring. But it's still dangerously weak.

Federal Reserve Chairman Ben Bernanke told Congress earlier this month that the economic recovery was "close to faltering." And the co-founder of the Economic Cycle Research Institute, a forecasting firm that predicted the last three downturns, said a recession was all but inevitable. Consumer confidence is the lowest in two and a half years.

"It almost looks like the world is worrying itself into another recession," Klaus Kleinfeld, the CEO of Alcoa, said Oct. 11.

One danger from Europe is that it could buy fewer U.S. goods. Europe buys 20 percent of U.S. exports.