I found this news item  http://electroniciraq.net/news/1184.shtml
It reports that :

"An independent review of US combat data, battlefield press reports, and Iraqi hospital surveys has found that approximately 13,000 Iraqis (plus or minus 16.5 percent or 2,150) were killed during the major combat phase of Operation Iraqi Freedom. The report covers the period from 19 March to the end of April. Among the Iraqi dead were between 3,200 and 4,300 noncombatants -- that is, civilians who did not take up arms.

The report, produced by the Project on Defense Alternatives at Commonwealth Institute in Cambridge, Massachusetts (USA), is the first to attempt a rigorous estimate of Iraqi military fatalities. It finds that 9,200 (plus or minus 1,600) Iraqi combatants were killed during the main combat phase of the war. This number it derives from operational statistics and the observations of embedded journalists and military personnel on both sides."

The non-combatant figure of about 4000 is less than the widely circulated figure from independent (ie non-US) sources of 7000-10000.

To try to see why there is this discrepancy, I accessed the full report, which you can find

as html :  http://www.comw.org/pda/0310rm8.html
as pdf :  http://www.comw.org/pda/fulltext/0310rm8.pdf

Here are some details:

Their overall conclusion is :
"Total Iraqi fatalities:  12,950  plus or minus 2,150 (16.5 percent)
Iraqi non-combat fatalities: 3,750  plus/minus 550 (15 percent)
Iraqi combatant fatalities:  9,200  plus/minus 1,600 (17.5 percent)"

In Baghdad alone:
"Combining the estimates for the various categories of war dead in Baghdad yields a total of between 4,376 and 5,526 fatalities, encompassing combatants and noncombatants, civilians and uniformed military:
Nominal civilian dead at hospitals: 2,876 + 
Military dead in military hospitals and wards: 500 - 1,200 
Unrecovered dead buried at Baghdad International Airport: 50 - 100 
Dead buried in ad hoc graves elsewhere in the city: 950 - 1,500 
Undiscovered dead: 0 - 50 
These estimates are based on a known -- that is recorded or counted -- quantity of at least 3,786 dead: 2,876-plus dead at civilian hospitals, 260 at the Rashid, 50 or more at the international airport, and 600 or more indentified by burial societies."

Examples on distinguishing non-combatants:

"A central issue in estimating civilian dead is separating combatants from noncombatants within this category. The conventional concern with civilian casualties stems from the presumed status of civilians as noncombatants. But the noncombatant status of civilians cannot be simply assumed.....
...the Al Karama hospital, where records also indicated that only
30 percent of the "probable civilians" were women or children. But this proportional distribution does not accord with the demographics of the general Iraqi population. A closer analysis suggests that as many as 45 percent of the "probable civilian" dead at Al Karama were actually combatants."

"Extrapolating from the sample at Al Karama hospital, we treat as combatants 44.4 percent of the entire category of 1,255 "probable civilians" reported by hospital officials to the Knight Ridder team. Thus, we regard 697 of these dead as noncombatants and 558 of them as combatants. The factors applied to other categories of the dead are pegged to this sample. "

".....we discount by 30 to 40 percent all the remaining dead categorized assuredly as "civilian" by doctors in the hospital surveys -- a category that comprises 1,621 dead...... Thus, of the 1,621 dead categorized by hospitals as assuredly civilian, we accept only between 973 and 1,135 as noncombatants. The remaining dead in this category, which number between 486 and 648, we count as combatants. "

"The estimates made by the burial societies and the Red Crescent warrant even greater care than the hospital records because the officials quoted seemed less systematic and rigorous in categorizing the dead"

It includes some painful descriptions:

"A factor that would have significantly influenced the balance of risk among the four noncombatant groups was the late exodus from Baghdad of thousands of Iraqi families. These civilians hoped to reduce their risks as the American assault on the city suddenly accelerated; instead, they inadvertently exposed themselves to the coalition onslaught.....
.....Although Iraqi officials continued to reassure residents that coalition forces would not enter the capital, few seemed convinced. In a grim e-mail from Baghdad on Sunday, Huguenin-Benjamin [of the International Committee for the Red Cross] described a "frenetic" scene Saturday morning as thousands of Baghdad citizens jammed the roads in taxis, cars and even horse-drawn carts.... "Entire families were moving from their homes," he wrote. "Families are camping overnight in their cars to escape the shelling."
The scene this describes was underway the day before the first US armored thrust into the city. The predictable result was that Baghdad civilians were killed or injured as American forces and firepower swept through sectors of the city and engaged Iraqi combatants. In one incident, at a south Baghdad interchange, two dozen civilian vehicles were inadvertently destroyed -- their occupants torn apart or incinerated -- by a US mechanized task force that was responding to an attack from nearby Fedayeen. Women and children were among the recognizable dead remaining in the wreckage days later."

Some extracts on Basra :

"The General Hospital in Basra reported 400 dead as of 7 April, the "majority of them civilians." The city's Teaching Hospital reported 200 dead. Together they reported almost 2,000 wounded. (Basra has four large hospitals, three of them major surgical centers of which the General and Teaching hospitals are two; all told the city has 11 hospitals, small and large."

"Basra ambulance drivers and hospital workers estimated handling between 1000-2000 corpses prior to the conflict's end. But this, presumably, is an estimate based on interviews with just a partial sample of the city's ambulance drivers and hospital workers."

Which lead to the rather strange conclusion :

" Considering these various data points it is likely that 700 or more Iraqis were killed in and around Basra during the war, although noncombatants would have been only a fraction of this total. And it is plausible that 700 deaths (and perhaps 2,000 injuries) would have been sufficient to create the impression among a subset of hospital and ambulance workers that their cohort had handled between "1,000 and 2,000 corpses"

Nasiriyah:

"There are four hospitals in the city. Near the war's official end the Saddam (now "General") Hospital in Nasiriyah -- one of two large ones in the city -- reported 713 dead.... An earlier report logged 250 civilians killed by aerial bombardment and artillery fire, which had prepared the way for more intensive ground action."

So one of four hospitals reports 700 (or is it 950 ?). Yet the conclusion is - no more than 300:

"The range of available estimates of the war dead in Nasiriyah makes it difficult to produced an estimate that is both highly precise and reliable. We have settled on an estimate of between 200 and 300 noncombatant dead. "

More numbers:
"Al Hillah: 105-120 noncombatant deaths"
"Najaf: 176-205 noncombatant fatalities"

Outside Baghdad:

"The Associated Press survey provides a complementary and more comprehensive source of statistics on the areas outside the five cities reviewed above. It accepted 906 recorded deaths of civilians in these areas. Because of the stringent criteria applied in the AP survey we accept between 60 and 70 percent of those it recorded as civilians to be noncombatants. This is between 540 and 630 fatalities.

Many smaller and more remote hospitals were excluded from the AP survey, however. A total of 94 hospitals and medical centers exist in the governorates other than Baghdad that saw some significant fighting. The AP team surveyed about 36 of these, presumably the largest and those reporting the highest casualty numbers. Although this sample is not complete, it may cover 75 percent of the beds in the relevant area and as much as 90 percent of the civilian hospital deaths. On this basis, we add an increment of 11 percent to our upper-range estimate of noncombatant fatalities outside Baghdad."

Overall the survey gives the impression of a very detailed and sophisticated analysis. It seems to me to contain a number of non-secquiturs such as are sampled above, as though perhaps numbers were altered near the end of its preparation. Maybe this in unfair - read it for yourself.

To form a real view, we would need to do a thorough detailed comparison of these people's assumptions, and those of other estimators. My impression is that their max figures are based on what seem to me less-than-maximum assumptions. But then, maybe I'm prejudiced.

Somewhere in the document (I can't find it now) I think I read an estimate of 40,000 Iraqis dead and injured.

Perhaps the difference between combatants and non-combatants is after all irrelevant. On the US's own interpretation, the combatants themselves were almost entirely unwilling, driven into the armed forces against their will be an implacable dictator who had crushed their every freedom. On that basis virtually all casualties were non-combatant in the sense that they were not fighting from choice.

The second half of this report is a rich mine of really detailed information on the weapons used by the US, their amount, and their effectiveness. Grim reading, but a report I think you should all download to preserve on your hard disks. My guess is it will soon be pulled.