In a clear sign that the glut is abating, oil in floating storage has plummeted in the past few months.
Although the oil stored in ships is a relatively tiny portion of world oil inventory, it is a good early indicator of what is transpiring in the murky physical oil market.
A rise in floating storage is driven by a confluence of cheap shipping and oil prices that are depressed near-term but higher long-term (known as a contango market), thus rewarding arbitragers who hang on to the oil rather than sell it on to end-user refineries.
"The contango market is no longer working and Dubai is in backwardation," said the Energy Aspects chief oil analyst Amrita Sen, referring to a market with higher prices for prompt versus future delivery.
Floating oil storage – defined as a full tanker docked for at least a week – "is a broad indicator to the extent there is a rebalancing and the crude overhang is being run down slowly", said Ms Sen, who added: "by no means is the crude overhang gone".
Tracking the physical oil market, including floating storage, is a highly imprecise science. It involves various competing analysts using methods ranging from satellite tracking and algorithms to individuals standing on the shore with binoculars.
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One of the big mysteries in the market is Iranian oil stored in offshore tankers, which is excluded from Energy Aspects' data.
Ellen Wald, an independent energy and geopolitics analyst, pointed out that there is dispute among analysts about how much Iranian oil is stored.
The estimates range from 30 million barrels to 47 million barrels, with the difference giving very different signals about how much oil Iran is capable of producing at present. It was a key question during tense negotiations within Opec about whether and to what extent Iran might be required to contribute to production constraint if they can agree a deal by the end of November.
"If Iran actually has had more oil in offshore storage than [some analysts] report, it could mean that Iran's production levels are less than otherwise believed and that its exports over the last few months have come from stored oil," Ms Wald said.
Still, the virtual disappearance of non-Iranian floating oil storage – from an estimated 75 million to 80 million barrels to about 10 million barrels – is supported by data from the largest consuming countries. Commercial inventories in the wealthy OECD countries fell in August for the first time since March, and early September data for Japan and the US showed the trend continuing, according to last week's report from the OECD energy think tank, the International Energy Agency.