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Operation IRAQI FREEDOM
From Citizendium, the Citizens' Compendium
Operation IRAQI FREEDOM is the official U.S. code name for the 2003 invasion of Iraq and continuing operations in the Iraq War. "IRAQI FREEDOM" was an after-the-fact name used to convey a positive image; the actual code name for planning was Operation POLO STEP. 
Officially, it ended when the 4th Stryker Brigade Combat Team, the last operational brigade in Iraq, left in August 2010.  Six other brigades actually remain, but they are called "advise and assist" units charged with training.