Brent crude was up 76 cents at $29.42 a barrel at the close of trading, up 2.8% from Tuesday's $28.66 close.
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Too much irreplaceable-in-the-short-term oil has been lost
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Energy analyst
US light crude, meanwhile, finished 65 cents higher at $31.85 a barrel.
The American Petroleum Institute (API) said on Tuesday, after the markets closed, that US reserves had fallen by more than 3% in the week ending 27 December because shipments from Venezuela - formerly the supplier of 13% of the US's oil needs - had stopped.
The world's leading oil markets, London and New York, were closed on Wednesday for the New Year holiday.
Oil reached a two-year peak on Monday of $33.65 before falling sharply after the Organisation of Petroleum Exporting Countries (Opec) said it would meet any shortfall in supply.
Supply problems
Venezuela, the world's fifth largest oil exporter, has shipped less than 10% of its usual output since an opposition strike to overthrow its democratically elected president began on 2 December.
"Too much irreplaceable-in-the-short-term oil has been lost, and the Iraqi situation is still out there," one Houston-based energy analyst told Reuters.
The US stockpile hit a 26-year low in October when storms disrupted oil operations in the Mexican Gulf.
The API report, which was released after the markets closed on Tuesday, is a key indicator for traders watching the world's biggest oil consumer.
Uncertainty about a US war with Iraq, and the possible disruption of Middle Eastern supplies, has also supported the high price of oil.
The international benchmark Brent crude oil in London fell $1.00 to close at $28.66 per barrel on Tuesday, having risen 44% in 2002.