An American patrol roared past us with the soldiers gesturing furiously with their guns for traffic to keep back on an overpass in central Baghdad. A black car with three young men in it did not stop in time and a soldier fired several shots from his machine gun into its engine.
The driver and his friends were not hit, but many Iraqis do not survive casual encounters with US soldiers. It is very easy to be accidentally killed in Iraq. US soldiers treat everybody as a potential suicide bomber. If they are right they have saved their lives and if they are wrong they face no penalty.
"We should end the immunity of US soldiers here," says Dr Mahmoud Othman, a veteran Kurdish politician who argues that the failure to prosecute American soldiers who have killed civilians is one of the reasons why the occupation became so unpopular so fast. He admits, however, that this is extremely unlikely to happen given the US attitude to any sanctions against its own forces.
Every Iraqi has stories of friends or relatives killed by US troops for no adequate reason. Often they do not know if they were shot by regular soldiers or by members of western security companies whose burly employees, usually ex-soldiers, are everywhere in Iraq.
A member of the Iraqi National Congress, Ahmed Chalabi's party, was passing through an American checkpoint last year when a single shot rang out from a sniper. No US soldier was hit, but the troops at the checkpoint hosed down the area with fire, wounding the INC member and killing his driver.
The rector of Al-Nahrain University in south Baghdad was travelling to a degree ceremony on the other side of the city when white men in a four-wheel drive suddenly opened fire, hitting him in the stomach. Presumably they thought he was on a suicide mission.
It was obvious to many American officers from an early stage in the conflict that the Pentagon's claim that it did not count civilian casualties was seen by many Iraqis as proof that the US did not care about how many of them were killed. The failure to take Iraqi civilian dead into account was particularly foolish in a culture where relatives of the slain are obligated by custom to seek revenge.
The secrecy surrounding the numbers of civilians killed reveals another important facet of the war. The White House was always more interested in the impact of events in Iraq on the American voter than it was in the effect on Iraqis. From the beginning of the conflict the US and British armies had difficulty in working out who in Iraq really was a civilian.
Marla Ruzicka, the American humanitarian worker who was buried yesterday in California, had established in her last weeks in Iraq that figures were kept based on after-action reports. Officially, she found, 29 civilians were killed in fire fights between US forces and insurgents between 28 February and 5 April. But these figures are likely to be gross underestimates.
US soldiers are notorious in Iraq for departing immediately after a skirmish, taking their own casualties but sometimes leaving damaged vehicles. They would not have time to find out how many Iraqis were killed or injured.
The Health Ministry in Baghdad did produce figures and then stopped doing so, saying they had not been properly collated. Iraqi Body Count, a group monitoring casualties by looking at media sources, puts the total at 17,384. But most Iraqis die obscurely; it is dangerous for reporters, Iraqi or foreign, to try to find out who is being killed. Much of Iraq is a bandit-ridden no-man's land.
Even in Baghdad it is evident from the hundreds of bodies arriving at the mortuary that this has become one of the most violent societies on earth. The Iraqi Body Count figure is probably much too low, because US military tactics ensure high civilian losses a bizarre aspect of the war is that US commanders often do not understand the damage done by their weapons in Iraq's close-packed cities.
US firepower, designed to combat the Soviet army, cannot be used in built up areas without killing or injuring civilians. Nevertheless, a study published in the Lancet saying that 100,000 civilians have died in Iraq appears to be too high. But the lack of definitive figures continues to dehumanise the uncounted Iraqi dead. As Dr Richard Garfield, a professor of nursing at Columbia University and an author of the Lancet report, wrote: "We are still fighting to record the Armenian genocide. Until people have names and are counted they don't exist in a policy sense."
The immunity of US troops means that there is nothing to inhibit them opening fire in what for them is a terrifying situation. For all their modern armament they are vulnerable to suicide bombers and roadside bombs. In the first case the attacker is already dead and in the second the man who detonates the bomb is probably several hundred yards away and in cover. With nobody else to shoot at it is the civilians who pay the price.