Global oil prices have remained around $61 a barrel after the weekend hanging of Saddam Hussein did not spark widespread violence in Iraq.
With mild weather in North America also subduing demand, a barrel of US light crude was down 20 cents at $60.85 in electronic trading on Tuesday.
Meanwhile, London's Brent crude slipped 42 cents to $60.44 a barrel.
Oil prices had climbed above $62 last month after producers' group Opec said it would cut output from 1 February.
The 11-member group has agreed to cut output by an extra 500,000 barrels a day, following a previous cut in November.
Chinese demand
Oil prices hit $78-a-barrel highs in mid-July last year at the height of the crisis between Israel and Lebanon.
Other factors that increased prices in 2006 were fears of trade sanctions against Iran, and unrest in Nigeria.
Analysts estimate that barring unforeseen events, oil should trade between $60 and $55 a barrel in 2007.
Global demand for oil has been boosted in recent years by China's fast-growing economy.
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