Despite official denials, Iran oil exports have plummeted some 40 percent in the past six months, to 1.5 million barrels per day (mbpd), according to the International Energy Agency (IEA).
Storage facilities and anchored tankers are close to saturation as Iran tries to avoid cutting production from its oil fields, several foreign experts in Tehran say.
The IEA said up to 42 million barrels of oil were being kept in the stationary tankers.
It added, in its latest Oil Market Report of June 13, it says Iran oil exports could fall further in the second half of this year. It cautioned that its data were preliminary, and were challenged by Iran "routinely" switching off mandatory tracking devices on its oil tankers.
Iran disputes the data and insists it is exporting 2.1 to 2.2 mbpd.
Oil Minister Rostam Qasemi was quoted by the ISNA news agency as saying on June 15: "Oil exports continue as before. Oil sanctions against Iran will have no negative impact."
The European Union, which up to last year imported some 600,000 bpd, or 20 percent of Iran's exports, announced on January 23 it would phase in its embargo which becomes fully effective on July 1.
On Monday, the EU citing "a review of the measures" confirmed the embargo would be enforced from Sunday.
Most EU member states have already implemented cuts, with Spain and Greece halting imports in April.
Italy, Europe's biggest importer of Iranian crude (180,000 bpd), is trailing but expected to follow suit within months, as soon as Iran delivers oil to Italian company ENI as reimbursement of a debt of hundreds of millions of euros.
European oil companies such as Shell and Total have suspended their contracts.
The EU embargo, imposed to pressure Iran to roll back its controversial nuclear programme, is coupled with US sanctions hitting Iran's financial sector.
On Thursday, the US measures will toughen when foreign companies that do business with Iran's oil sector will be threatened with US penalties unless their countries are granted exemptions on the basis of Iran oil import cuts.
Turkey, Iran's neighbour to the north and its fifth-biggest oil customer, has made its sole refiner, Tupras, agree to trim Iran crude oil purchases by 20 percent and instead source from Libya.
South Africa, another important customer, has also gone with other suppliers.
In Asia, which absorbs 70 percent of Iran's oil exports, the situation is mixed.
India, Iran's number two customer, has announced an 11-percent cut to Iran oil imports this year, and South Korea, the third biggest customer, has axed 40 percent from its Iran input.
Japan, the fourth-biggest customer, slashed Iran oil imports by 65 percent in April while boosting shipments from Saudi Arabia.
But China -- the top buyer of Iranian crude -- has reportedly recently been bringing its imports back up towards its previous 400,000 bpd level after a dip earlier this year attributed to a row with Iran over prices and payment.
Beijing steadfastly refuses to cede to the US pressure.
Even where Iran is still selling its black stuff, repatriating the petrodollars generated -- and they amounted to $100 billion in 2011 -- is increasingly problematic because of the US financial squeeze.
Tehran is now accepting payment in other nations' currencies, or is resorting to bartering its oil for food and goods.
And to ensure oil exports to some destinations, Iran is offering discounts of up to $20 per barrel to countries such as Pakistan, one European oil executive said.
It is even using its own tanker fleet to deliver crude, to get around the problem of cargo insurance posed by the looming EU embargo, according to international oil experts.
Another blow to Iran's vital oil export revenues comes from the price for oil.
After a skyrocketing rise to a March peak, prices have tumbled to $90 a barrel for Brent reference crude. Analysts believe they could fall further this year as Europe's debt crisis deflates the global economy.
That is far away from Iran's predictions that the world would be unable to cope with reduced Iranian oil exports, and that the price would jump to $150 a barrel.
"Iran hopes a price rise will compensate for its lowered exports, but increased production in other countries, especially Saudi Arabia, have allowed a gradual phase-in of the embargo that has not destabilised the market," one European expert said in Tehran.
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Iran's supreme leader Ayatollah Khamenei should know his priorities better. The theocratic regime could survive without nuclear weapons, but not without the oil revenues. Unfortunately ordinary Iranians have to bear the brunt of these economic sanctions. Popular dissent might prove the regime's undoing.