Oil fell to around $80 a barrel after a steep decline in U.S. crude inventories sent prices up 1 percent the previous day, as traders aimed to lock in profits amid weaker equity markets and a firming dollar.

U.S. crude for December fell 45 cents to $79.95 by 1151 GMT, after hitting $81 a barrel the previous day.

London Brent crude fell 51 cents to $78.38 a barrel, after settling up 80 cents on Wednesday.

The dollar is up and equities are down -- there you go. The correlation seems to be holding, said Global Insight analyst Simon Wardell.

He added that prices seemed overbought at current levels. Prices probably overcorrected at the end of last year but there's quite a bit of froth now.

News of a surprise 4 million barrel drop in U.S. crude stocks last week sparked a rally on Wednesday which saw prices jump to within a dollar of the October 12-month high of $82 a barrel.

The U.S. Federal Reserve's decision to keep borrowing costs near zero for an extended period on Wednesday also weighed on the dollar and raised expectations that demand in the main fuel consumer would improve, spurring oil prices higher.

But the rally lost momentum on Thursday and prices turned negative as the dollar moved higher and European equities fell.

A stronger dollar makes oil more expensive for holders of other currencies.

With energy's supply/demand outlook in poor shape, the bulls need to rely on a progressively weaker dollar to keep the rally going, said MF Global Energy analyst Edward Meir in a research note.

External factors such as equity markets and the dollar have been largely responsible for this year's price rally which have seen prices double since lows near $40 a barrel in January.

Analysts also said that closer scrutiny of the U.S. stocks data from Wednesday suggested a bleaker demand outlook than the crude oil data revealed.

U.S. distillate stocks -- often taken as a more faithful snapshot of demand -- fell 400,000 barrels compared to analyst expectations for a 1 million barrel decline. They remain near 26-year highs and analysts said this will cap price rises in the event of a cold winter.

Energy traders will look to jobs data on Friday at 1330 GMT for further clues about the demand picture in the world's largest fuel consumer.

U.S. employers in October cut payrolls by the smallest amount in 14 months as the economy's resumption of growth boosted optimism, but the jobless rate rose to a fresh 26-year high, a Reuters survey predicts.

(Additional reporting by James Topham in Singapore; editing by Keiron Henderson)