* Dollar falls broadly, early 2011 outlook brighter
* Euro zone debt worries still on investors' minds
* Yen hits seven-week high; some see losses ahead in 2011
* Swiss franc hits new peak against the dollar (Updates prices, adds comment)
By Steven C. Johnson
NEW YORK, Dec 31 (Reuters) - The dollar fell broadly on Friday as investors closed their books on 2010, but it still managed to end a volatile year a bit firmer than where it began, with the improving U.S. economy outlook leaving some traders gearing up for a rally in early 2011.
The euro rose 1 percent to $1.3394 <EUR=>, extending its recovery from a 2010 low beneath $1.19 -- its worst showing since early 2006.
But it was set to end the year down 6.5 percent against the dollar, hurt by a debt crisis that engulfed Greece and Ireland, rattled Portugal and Spain and even sowed doubts about the euro's future. It was its biggest annual slide since 2005.
The yen, however, rose about 12 percent against the dollar this year as long-term U.S. interest rates fell and markets feared a sluggish U.S. recovery was running out of steam.
On Friday, the dollar fell 0.5 percent to 81.16 yen <JPY=>, its lowest since early November.
For the year, the dollar was up about 1.4 percent against a basket of currencies <.DXY>, though it was 0.7 percent lower on Friday after hitting a seven-week low against the yen and a record low against the Swiss franc.
Still, analysts expect a more durable U.S. economy and Europe's debt crisis to spark dollar gains in early 2011.
SUNNY GROWTH OUTLOOK
U.S. manufacturing and consumer data has improved in recent months and the private sector has started adding more jobs, though the unemployment rate remains high at 9.8 percent.
"We're still facing a lot of uncertainty next year, but the U.S. economic data is starting to turn for the better and I think that will spark dollar gains, particularly against the yen," said Boris Schlossberg, research director at GFT Forex.
The United States will release December employment data next Friday, and economists polled by Reuters expect to see a private sector job gain of 140,000.
Schlossberg said higher U.S. bond yields in 2011 and Japan's increased reliance on debt will eventually put pressure on the yen, which neared 80 per dollar earlier this year, just shy of a post-World War II high of 79.75 yen set in 1995.
UBS strategist Geoffrey Yu said expectations for more robust U.S. growth means U.S. securities are likely to continue their trend of attracting strong inflows in January, and that should provide a near-term boost for the greenback.
The Australian dollar, which hit a 28-year high of $1.0257 <AUD=D4> on Friday and was up 14 percent against the greenback this year, may also extend gains if global growth remains firm and commodity prices high. But a slowdown in China is a risk, and some analysts said the Aussie's 2010 gains may make it ripe for a correction next year.
THE EURO'S STRUGGLES
Traders tied much of the dollar's losses this week to thin volume and year-end positioning, with many investors taking profits on extended bets against the euro that have built up over recent months as fears of a euro zone debt crisis grew.
The euro's repeated inability in recent weeks to hold below a 200-day moving average, now at $1.3085, has also contributed to recent gains. Traders cited buying by Asian central banks and real money accounts.
The euro may remain under pressure early in 2011 as an estimated 150 to 200 billion euros in euro zone sovereign bonds come to market, and some investors worry demand may be weak.
"Everybody, it seems, is anticipating a very rocky road for the euro zone over the next three months," said Gareth Berry, G10 FX strategist for UBS in Singapore.
FRANC TO COME BACK TO EARTH?
Some traders said these concerns and more muted worries about U.S. finances have contributed to Swiss franc gains.
Despite signs of stronger U.S. growth, the Federal Reserve has given no indication that it plans to curtail a $600 billion bond-buying program it started last month. Analysts also fear a deal to extend U.S. tax cuts could swell the budget deficit.
The dollar set a record low of 0.9302 francs <CHF=EBS> on Friday before easing back to 0.9339. The euro hit a 1.2398-franc record low Thursday before rebounding to 1.2509.
While Schlossberg extolled Switzerland's fiscal health and called the franc "arguably the only sound money left" among major currencies, he said recent gains are excessive.
"It's just not sustainable that a country of 7 million can absorb the capital flows they've been absorbing," he said. (Additional reporting by Anirban Nag in London; editing by Dan Grebler)