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. What they do with that time will determine whether this summit succeeds where many others have failed.

Thursday's three-pronged deal at long last appears to have met or beaten expectations for some kind of decisive action, judging by stock market rallies in Europe and around the world. It retools the eurozone's underpowered bailout fund, calls on banks to take 50 percent losses on Greek bonds and orders them to raise €106 billion in new capital by June.

"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.

But European leaders will have to work out the complex financial details quickly and skillfully. It's unclear whether the bailout fund changes will be enough to prop up Italian and Spanish banks, or whether the bond writedown will be enough to pull Greece from the brink.

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 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.

The respite could be short if they return to the fudges and procrastination that have so far marked their response to the crisis, which broke out just over two years ago 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.

The hope now is that the trio of measures crafted in Brussels on Wednesday and Thursday 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.

The most difficult part of the plan was persuading banks to take 50 percent losses on their Greek bonds to make the country's debt pile small enough for Greece to be capable of repaying it. But even that massive "haircut" might not be enough.

The deal will cut Greek debt to 120 percent of economic output by 2020, from 180 percent otherwise. Yet debt of more than 100 percent of GDP is still breathtakingly high.

European leaders agreed to push Europe's banks to raise €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.

The €440 billion ($610 billion) bailout fund - the European Financial Stability Facility - will be reworked to make its firepower equivalent to around €1 trillion ($1.39 trillion), to make it better able to help large but wobbly countries such as Italy and Spain.