The civilians of Falluja are negotiating to stave off a threatened US-led military incursion. American military spokesmen insist that US-led forces will do their utmost to spare civilian bystanders. But if they don’t, the newly free Iraqi press will have trouble reporting the story. The Iraqi Health Ministry, on orders of the US-backed government, has stopped releasing Iraqi casualty figures to journalists. The ministry’s numbers had been turning up in news reports, most notably in a Knight Ridder story on how many Iraqi civilians have been killed in recent fighting, which was widely distributed in the United States.

So the problem of Iraqi civilian casualties reverberates in the troubled US military occupation of Iraq. But what isn’t known about ordinary Iraqis dying from US firepower is a big part of that problem. The Pentagon shows no interest in the subject. “We don’t do body counts,” Gen. Tommy Franks has famously said. And in the chaos of Iraq, reporters and public health authorities simply can’t keep track. This isn’t just a problem for the Iraqis whose lives are at risk. It’s a problem for Americans trying to figure out how the military is going to overcome the hostility it now faces in Iraq.

On the subject of civilian casualties, Americans lack what they usually love: a nice round number that endows an emotional issue with numeric authority. In September the talisman figure of 1,000 US combat deaths became the emblem of growing national doubts about the war in Iraq. But all the experts on Iraqi civilian casualties argue persuasively that there is no comparably accurate figure that might sum up the suffering of the Iraqi people.

On October 19, the New York Times took a step toward settling on a civilian casualty number by reporting that “the best estimates” of private groups and independent news organizations are in “the 10,000 to 15,000 range.” That is comparable to the figure given by iraqbodycount.net, a website run by US and British antiwar activists, which gives a low estimate of 13,928 civilian deaths in Iraq and a high one of 16,053. The site’s researchers carefully monitor news reports of civilians killed in warlike incidents and because of breakdowns in law and order and healthcare and sanitation problems, weed out stories that appear in only one place and add up all casualties.

Complaints about the group’s reliance on media sources are overblown. The bigger problem is that Iraq Body Count’s figures do not distinguish between Iraqi civilians killed by US troops and Iraqis killed by jihadists. The site’s founders say that, as an occupying power, the United States is responsible under the Geneva Convention for all violence suffered by Iraqi civilians. The result is confusion. According to the Iraq Body Count methodology, if the Iraqi insurgency killed twice as many civilians as US Marines next month, all of those deaths would be chalked up to Washington’s policy. That may be morally satisfying, but it doesn’t really measure how US soldiers are treating Iraqi noncombatants. The Iraq Body Count number is more reliable as an index of Iraqi chaos than civilian casualties of US force.

But there’s another way to gauge civilian casualties, and that is to consult not the media and not human rights groups but US troops themselves. That’s what a team of six mental health specialists did last year. In a study published in the July 1 New England Journal of Medicine (NEJM), they asked two groups of Army and Marine troops about what they had seen and done in Iraq. The results of this survey suggest that the Times estimate of Iraqi civilian casualties, like the Iraq Body Count number, is too low. The number of civilian casualties inflicted by US forces may be underestimated, even by the liberal press and war critics.

Asked if they had ever killed an Iraqi noncombatant, 28 percent of the 794 Marines surveyed said yes. Two-thirds reported killing an enemy combatant. Fourteen percent of 861 soldiers from the Army’s 3rd Infantry Division reported they had killed at least one Iraqi noncombatant. Forty-eight percent reported killing an Iraqi combatant. These troops, it should be added, also reported significant rates of heroism. Nineteen percent of the Marines said they had saved the life of a soldier or civilian. Twenty-one percent of the soldiers said the same.

The NEJM survey offers what no other study of Iraqi civilian casualties provides: a sense of the prevalence of lethal violence inflicted on Iraqi civilians, as seen by US troops themselves. The troops surveyed were typical of US forces as a whole. The demographic characteristics were “very similar to those of the general, deployed, active-duty infantry population, except that officers were undersampled,” according to the authors. These soldiers served under fairly typical conditions for combat units. The 3rd Infantry Division and the 1st Marine Expeditionary Force participated in the march to Baghdad and also experienced the eruption of the Iraqi insurgency in the summer and fall of 2003.

Two qualifiers need to be added. First, the NEJM study suggested that only 25 percent of US forces faced the same type of combat situations as these units. Second, these soldiers described civilian casualties in six- to eight-month deployments. The resulting figures need to be extrapolated to a conflict now it its twentieth month. But if you adjust the numbers to reflect those realities, and if the Army and Marine combat troops killed civilians at the same rate as their comrades in the NEJM study, then US ground combat forces would have been responsible for the deaths of an absolute minimum of 13,881 noncombatants since March 2003. And that figure omits all civilian deaths caused by the Air Force and by noncombat Army and Marine forces.

Needless to say, this figure is a suggestive estimate, not a definitive number. And a third caveat is necessary. Iraq was also a very deadly place for many civilians under the reign of Saddam Hussein. The Iraqi dictator killed an estimated 300,000 people during his twenty-four-year reign, an average of 12,500 a year. In other words, the NEJM survey suggests that US military power may now be more hazardous to the health of Iraqi civilians than the dictatorship it destroyed.