And as it has grown more pervasive, so it has become more organised and ingenious.
Investigators describe a chain starting with looters who steal to order, deliver artefacts to local merchants, who smuggle them out of Iraq to dealers connected to wealthy collectors in the Middle East, Asia, Europe and the United States.
The most sought-after items include cuneiform tablets -symbol-rich clay palettes that contain the origins of writing -cylinder seals, which were used to identify or mark ancient documents, intricate figurines and items of bronze jewellery.
Hamdani says looters - generally penniless villagers familiar with the locations of the sites - get as little as $13 for a whole cuneiform tablet.
"It will be sold on for tens of thousands of dollars, but really it is priceless," he said, shaking his head at the damage inflicted on Dubrum.
In the year since US-led forces invaded Iraq, the focus of attention has been on battling a determined resistance and restoring security. But bit by bit, attention is also being paid to stopping desecrations like archaeological looting.
Italy, one of the closest US allies in Iraq and a country with a history of fighting organised crime, has sent units of its Carabinieri paramilitary force to lead the battle to protect sites in a large swath of southern Iraq.
With several hundred sites to monitor in Dhi Qar alone the task appears far beyond the capacity of a force that numbers in the hundreds.
Instead, the Carabinieri have concentrated on securing the most important areas and are trying to patrol as many others as possible.
At the same time, they are training Iraqis to protect major sites and collect information on looting habits.
Often it is a cat-and-mouse game, with robbers growing familiar with the Carabinieri's techniques and sometimes getting warning of their approach - not difficult when they arrive across miles of open desert in convoys of armoured cars.
Only by using helicopters in flash raids and with an element of surprise have they managed to catch thieves red-handed.
Increasingly looters work at night. Sometimes they raid sites just beyond the Italians' strictly defined area of responsibility, betting they won't stray out of the zone.
In the eight months since the Italian specialised unit began its operations, only 47 robbers have been caught, although precious objects have also been rescued.
"There are more than 700 sites and there are a million
potential looters," Hamdani said. "Whatever we do is not
A year ago, in the immediate aftermath of Saddam's overthrow, the National Museum in Baghdad was the focus of
Gangs of looters broke into the museum and stole hundreds of priceless artefacts - ancient statues, low-relief carvings, Akkadian jewellery and Sumerian cylinder seals.
Many of the most important pieces, including the fabled treasures of Nimrud, have been recovered or were found stashed safely in the vault of Iraq's central bank.
Since most of the museum pieces were catalogued, it has even been possible to track down many of those that were spirited abroad.
Court cases are pending in the United States and Switzerland to recover several that are still missing.
But the same process cannot be used with ancient treasures that no one yet knows ever existed. For archaeologists and art historians it is an unfathomable loss excruciating to bear.
"To lose those objects is to lose the source of our identity, it's like losing the mother of civilisation," said Mario Bondioli-Osio, senior adviser to the Iraq's Ministry of Culture and formerly the president of Italy's commission for the recovery of stolen art.
Bondioli-Osio has been frustrated by the lack of attention paid to the problem with the U.S.-led coalition having to focus instead on combating the year-long insurgency.
With more funding and training, he says, a stop could be put to the thieving.
Iraqis need to be taught how to police ancient sites, they need weapons and communications equipment. A recent tightening of Iraq's borders was a positive step, he said.
Just a week ago, Jordan announced it had seized some 700
pieces smuggled out of Iraq and would return them.
For archaeologists, Iraq, often referred to as the cradle of
civilisation, offers the richest possible vein for discovery.
Some say the world's archaeology books could be rewritten
after just a few years of excavation in the country.
That will be impossible if the looting continues.
"We risk losing our understanding of how civilisation came
into being," said Bondioli-Osio, his face tense with concern as
he showed visitors around Baghdad's shuttered national museum.
"It is a rape of our humanity."