Brent crude oil futures were up 36 cents at $40.62 a barrel at 0951 GMT. U.S. West Texas Intermediate (WTI) crude futures were at $37.86 per barrel, up 35 cents from their last settlement.
U.S. crude was supported by a surprise 1.9-million-barrel fall in U.S. crude inventories to 488 million barrels last week.
The drop, as estimated by industry group the American Petroleum Institute, compared with analysts' expectations for an increase of 252,000 barrels.
Official figures from the U.S. Energy Information Administration (EIA) are due at 1530 GMT (1030 EST).
Japan's core machinery orders unexpectedly jumped in October and reforms aimed at encouraging imports in China, including of energy-intensive machinery helped improve the outlook for Asian demand.
However a strong dollar, weakening demand, soaring supplies, and expectations of a U.S. rate rise kept investors wary of further weakness.
"There was somewhat more positive data, but OPEC is not going to support the market and I think there's a high probability that we will break through the lows of 2008," said Bjarne Schieldrop, chief commodities analyst at SEB in Oslo.
Brent oil fell to just above $38 per barrel in December 2008.
On Tuesday, Brent touched its lowest levels since February 2009.
Oil slumped after OPEC last week failed to agree a cut in production quotas in the face of slumping prices and a mounting global supply glut.
"Brent crude prices will continue to struggle due to a large global commercial oil stock surplus, which PIRA estimates will total 500 million barrels above normal levels by end-2015," PIRA Energy said, adding that it expects onshore crude oil storage to run out in the first quarter of 2016.
Goldman Sachs said that it was "underweight commodities on a three-month basis, mainly due to downside for oil" but the bank added it was "less bearish over 12 months."
The outlook of slightly higher prices towards the end of 2016 is based on the expectation that some producers, especially U.S. shale drillers, will cut output due to low prices and as most established producers like Russia and OPEC are close to maximum production capacity.
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