West Texas Intermediate crude futures were up $0.31 at $57.93 a barrel by 0829 GMT.
Brent crude futures gained $0.53 to $64.88 a barrel. Both benchmarks had shed more than 3% on Tuesday.
Crude inventories fell by 1.4 million barrels last week till July 12 to 460 million barrels, the American Petroleum Institute (API) said on Tuesday. That compared with analyst expectations for a drop of 2.7 million.
The smaller-than-expected decline suggested production shut-ins caused by Hurricane Barry late last week had little impact on inventories.
Gasoline stocks also fell, the API data showed, but less than expected, and distillate inventories rose more than forecast.
Official data from the US government's Energy Information Administration (EIA) is due at 1430 GMT. If confirmed, it would be the fifth consecutive weekly decline, the longest stretch since the beginning of 2018.
More than half of daily crude production in the Gulf of Mexico remained offline on Tuesday in the wake of Hurricane Barry, the US drilling regulator said, as most oil companies were re-staffing facilities to resume production.
The Bureau of Safety and Environmental Enforcement said 1.1 million barrels per day of oil, or 58% of the region's total, and 1.4 billion cubic feet per day of natural gas output remained shut.
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