More than 1,600 US soldiers have been killed since the invasion of Iraq in March 2003. Other coalition allies are mourning dozens of their own fighting men and women.
There is no official record of how many Iraqi civilians have died
Thousands of Iraqi civilians have also died as a result of conflict and its bloody aftermath - but officially, no one has any idea how many.
Human rights groups say the occupying powers have failed in their duty to catalogue the deaths, giving the impression that ordinary Iraqis' lives are worth less than those of soldiers.
Unofficial estimates of the civilian toll vary wildly, from at least 10,000 to about 100,000.
But the view famously expressed by US General Tommy Franks that "we don't do body counts" still resonates in government circles.
America and Britain say the chaos of war-torn Iraq makes it impossible to get accurate information.
And while Iraq's health and interior ministries now record non-military deaths, resources for this are tiny in a country rebuilding after war.
The AFP news agency has started compiling casualty figures for Iraq based on information from Iraqi ministries.
The agency estimates that 364 civilians died in April 2005 from car bombings, bomb explosions and shootings.
Iraq Body Count
The UK-based Iraq Body Count - run on a shoestring by about 20 academics and peace activists - is one of the most widely-quoted sources of information on the civilian toll.
It says 22-25,000 ordinary Iraqis have died since the invasion in March 2003 - figures compiled from media reports of thousands of incidents.
Civilian toll estimates at 05/05
Iraq Body Count: 22-25,000
The Lancet: 100,000
UK foreign secretary: >10,000
People's Kifah >37,000
Where sources report differing figures, a minimum and a maximum are given.
Professor John Sloboda, a co-founder of Iraq Body Count, told the BBC News website: "Everyone can agree that there are good reasons why our count can never be complete, but there is not as much confusion as you think.
"Since the end of hostilities was declared, we are confident in the figures."
The IBC wants to see an independent commission set up in Iraq to give the best estimate of civilian deaths and full details of how each person died.
Prof Sloboda said: "No country could hold its head up high without looking back to investigate the deaths of thousands of its people.
"Imagine the United States not investigating exactly who died on 11 September, it is unthinkable."
Other sources for casualty figures include the Washington-based Brookings Institution, which combines IBC's figures with projections for deaths caused by violent crime in Iraq.
In June 2005, it said that between May 2003 and 30 April 2005 6,598 Iraqi civilians had been killed in acts of war. This number does not include Iraqi civilians killed during what the US military defined as "major combat operations" between 19 March and 30 April 2003.
A study by the British medical journal, the Lancet, estimated in October 2004 that the invasion of Iraq had led to the deaths of 100,000 beyond what might have been expected before the invasion.
In August 2004, an Iraqi group calling itself the People's Kifah said it had
documented more than 37,000 civilian deaths from March to October 2003. But there has been no independent scrutiny of these figures.
The Pentagon, like the UK Ministry of Defence, maintains US forces do all they can to minimise civilian casualties in one of the "most precisely targeted campaigns" in history, but it has said it does not produce figures on those killed.
A UK Ministry of Defence spokesman said: "It should be recognised that there is no reliable way of estimating the number of civilian casualties caused during major combat operations.
"We would caution against taking the numbers quoted in media reports and else where at face value. No source or combination of sources can produce a reliable figure."
But in May 2004, UK Foreign Secretary Jack Straw told BBC radio that estimates by non-governmental organisations put the civilian death toll at about 10,000 in the year after the invasion. He said it was "odd that coalition forces have not kept consistent records".
The Foreign Office now says 10,000 was never an official figure, and doubts one will ever be obtained.
'Weigh cost of war'
Critics point to the fact that neither the British nor US forces have any difficulty in announcing they have killed a fairly exact number of "enemy" or "insurgents".
Outcry over civilian deaths in other conflicts has shaped military policy
And some legal experts say it is the duty of occupying powers to keep track of civilian losses under the Geneva Conventions.
But in many incidents it is hard to get a true picture of what caused the attack, let alone how many people were killed.
Ken Roth, head of Human Rights Watch, told the BBC News website he did not think it would ever be possible to come up with anything better than a good guess at the final civilian cost.
"It's not like Yugoslavia where the Serbs kept detailed records of the civilian toll. In Iraq, the institutions that could have compiled them have broken down.
"In the chaos of Iraq, people die, they are quickly buried and nothing more may be heard of them. Fighters dress in street clothes, so in hospitals they are indistinguishable from civilians."
Producing a final toll can be useful in that we can weigh the cost of war against the number of innocent lives, Mr Roth said.
"But what is more important is what lessons can be learned by investigating how and why people were killed."
Human Rights Watch says the invasion of Iraq saw a dramatic fall in the number of US Air Force strikes using cluster bombs in populated areas - a consequence of lessons learned in Afghanistan.
But it says the US Army - which had not fought a major war for 10 years - continued to use the controversial bombs in abundance.
A recent HRW report also criticised what it said was the "imprecise targeting" of decapitation strikes against figures in Saddam Hussein's regime.
Out of 50 strikes, none were hit, says HRW, but 40 civilians were killed because planners relied on rough Global Positioning System locations from mobile phones.
"Any attacking force has a duty to do this kind of analysis," said Mr Roth. "What is amazing is that the US does nothing of the sort."
In the meantime, Iraq's precarious security situation sees dozens of people killed every day.
"Nobody can stop themselves being drawn into the blind violence that continues to sweep the country," said Nada Doumani, of the International Committee of the Red Cross.
"Civilians are those who pay the greatest price."