EU Allowances for Dec-10 delivery lost 6 cents or 0.5 percent at 12.68 euros a tonne on light volume of just over 250 lots traded by 0922 GMT.
The market's down a bit on German power, but we're seeing what can be best described as 'nothing', said one trader.
German Calendar 2010 baseload power fell by 55 cents or 1.2 percent at 43.95 euros per megawatt hour.
Spot European power prices eased on Monday in thin trading on the back of lower consumption during the Christmas holidays and milder temperatures, traders said, adding supply was ample.
U.S. crude oil futures held steady below $79 on Tuesday, after hitting a five-week high a day earlier, as the firm dollar offset colder U.S. weather and expectations of a further drawdown in crude inventories.
Oil is up nearly $10 or some 13 percent since December 14.
Dec-10 CERs traded down 5 cents or 0.5 percent at 11.17 euros a tonne on light volume of 37 lots.
The EUA-CER spread edged up to around 1.55 euros.
With just two and a half trading days left in 2009, benchmark EUAs are down 3.22 euros or 20 percent for the year.
The front month Phase 2 (2008-12) contracts hit a 2009 high of 16 euros on May 12, a far cry from the record high of 29.69 euros on July 2, 2008. The futures are up some 58 percent since bottoming out at a record low of 8.05 euros on February 12, 2009.
The European Climate Exchange will close at midday on Thursday for New Year's Eve and remain closed on Friday. (Reporting by Michael Szabo; editing by James Jukwey)