The death count is NOT under 2000. Here are the numbers the Associated Press is leaving out.
According to the Department of Defense these are the official numbers:
Operation Iraqi Liberation (OIL):
Combat Ops 3/19/03 to 4/30/03 - 139 Deaths
Post Combat Ops 5/1/03 to 10/21/05 - 1,839 Deaths
DoD Civilians - 5 Deaths
Total: 1,983 Deaths