* Copper steadies after sharp loss, other metals fall
* U.S, German bond yields fall as investors move to safe assets
* Wall Street's main indexes gain modestly
* Oil falls as U.S. fuel stock build signals easing demand (Updates with open of U.S. markets; changes dateline from London)
NEW YORK, Dec 6 (Reuters) - A gauge of global stocks fell on Wednesday and benchmark government bond yields declined as investors weighed signs of risk in the markets and with U.S. policy.
MSCI's gauge of stocks across the globe shed 0.36 percent, while Wall Street's main indexes edged higher in choppy trading.
Stocks have paused after getting a fresh leg to their record-setting rally, fuelled by improving prospects for a U.S. bill that would slash corporate taxes.
But investors are now waiting to see the final tax legislation, while a potential U.S. government shutdown looms if Congress fails to agree on a spending package.
At the same time, markets have flashed some concerning signals. Copper, which is seen as an indicator of global demand, posted its biggest decline in more than two years on Tuesday, while the U.S. yield curve between two- and 10-year Treasuries continued to flatten, another potential indicator of worries about the economy.
There are some inconsistencies in the market right now with what appears to be a very positive economic backdrop, said Walter Todd, chief investment officer at Greenwood Capital Associates in Greenwood, South Carolina.
The Dow Jones Industrial Average rose 12.89 points, or 0.05 percent, to 24,193.53, the S&P 500 gained 1.66 points, or 0.06 percent, to 2,631.23 and the Nasdaq Composite added 12.22 points, or 0.18 percent, to 6,774.43.
Areas such as banks, transports and telecoms, expected to benefit from lower corporate taxes, have rallied as prospects for the legislation improved.
In Europe, the pan-European FTSEurofirst 300 index lost 0.01 percent.
U.S. Treasury yields fell across the board as risk appetite slid, while German 10-year government bond yields hovered near three-month lows.
"This market is like a junkie, waiting for the next fix," said Bruno Braizinha, interest rates strategist at Societe Generale in New York.
"All the good news seems to have been priced in: the U.S. tax reform, the Federal Reserve hike next month and next year. So now the market is waiting for the next positive thing," he added.
Benchmark 10-year notes last rose 9/32 in price to yield 2.3242 percent, from 2.356 percent late on Tuesday.
The dollar index rose 0.21 percent, with the euro down 0.3 percent to $1.1789.
Copper steadied after its sharp falls in the previous session, while other metals fell on concerns that China could see a weaker first half of 2018 and as investors looked to reduce their long exposure before the end of this year.
Copper rose 0.34 percent to $6,565.50 a tonne, after falling more than 4 percent on Tuesday.
Oil fell after a sharp rise in U.S. inventories of refined fuel suggested demand may be flagging, while U.S. crude production hit another weekly record.
U.S. crude fell 1.98 percent to $56.48 per barrel and Brent was last at $61.80, down 1.69 percent on the day.
Spot gold dropped 0.2 percent to $1,263.61 an ounce.
(Additional reporting by Gertrude Chavez-Dreyfuss in New York, Helen Reid in London; Editing by Catherine Evans and Nick Zieminski)