Oil bulls got their first ray of hope last week from the U.S. Energy Information Administration. Weekly data showed a sharp fall in inventories, appearing to support the notion that OPEC is finally taking chunks out of the global crude glut.

But surging exports from North America mean the market should treat that idea with some caution. Stockpiles aren't coming down because the oil is being used, it's just being moved overseas.

The EIA reported the biggest drop in combined crude and refined-product stocks (including those held in the Strategic Petroleum Reserve) in four years for the last week of June.

In the four months through June, when any cuts in OPEC crude deliveries to the U.S. should have begun to show up in lower import numbers, the oil stockpile tumbled by almost 21 million barrels.

That doesn't seem like a lot. At that rate, it would take two-and-a-half years to get total inventories back to their five-year average level.

It does start to look better, though, if you compare that with what normally happens over the period.

This is the first year since at least 2000 that total U.S. oil inventories have fallen between the end of February and June 30. The average increase in stockpiles over that period has been 54 million barrels.

Sure, that average is inflated by some abnormally large builds for various reasons, but even stripping those out, the increase is 37 million barrels. It's really that number that we should be comparing against this year's 21-million-barrel decrease. A 58-million-barrel draw looks much healthier, and would get stockpiles down in around 11 months.

But what has happened to all that oil?

U.S. demand did hit a record in the last week of June, but more than half of the week-on-week increase came from the volatile "other oil products" category, not core fuels like gasoline, diesel or jet fuel. In fact, gasoline demand has lagged last year's level all year and still shows little sign of exceeding it.

The short answer is that the oil has been sent elsewhere.

The U.S. is a big net importer of oil -- dreams of energy independence have yet to be realized -- but the excess of imports over exports has slipped after the ban on overseas sales was lifted last year. The U.S. exported 149 million more barrels of crude and refined products in the four months through June than it did in the same period of 2016. Had those barrels not been exported, U.S. inventories would have risen by another 129 million barrels.

Does this matter?

Yes, because the surge in U.S. exports is contributing to the robustness of inventory levels elsewhere. Stocks in the key European storage hub in the Amsterdam-Rotterdam-Antwerp region are up 5.5 million barrels since the end of February, data from Genscape show.

Chinese government data show commercial stockpiles almost unchanged between the end of February and the end of May, yet oil exports to Asia's biggest economy have soared. In the first four months of 2017, 55 million barrels of crude and products flowed from the U.S. to China -- more than the first nine months of 2016.

Facts Global Energy, a London-based consultancy, estimates that global oil inventories on land are "no lower now than when the output cutback deal was implemented in January." What's more, a reduction in the volume of oil stored on tankers has been entirely offset by an increase in the volume in transit.

Oil bulls will probably welcome the big drop in U.S. inventories. But it's too early to send the bears into hibernation.

This column does not necessarily reflect the opinion of Bloomberg LP and its owners.

Julian Lee is an oil strategist for Bloomberg First Word. Previously he worked as a senior analyst at the Centre for Global Energy Studies.