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Operation Phantom Fury: The Assault and Capture of Fallujah, Iraq by 
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Major battle fought in and around the city of Fallujah, some 42 miles west of Baghdad, between U.S., Iraqi, and British forces and Iraqi insurgents (chiefly Al Qaeda in Iraq but also other militias). Following the decision to halt the coalition assault on Fallujah in Operation Vigilant Resolve (the First Battle of Fallujah) during April-May 2004, the U.S. marines had withdrawn from the city and turned over security to the so-called Fallujah Brigade, an ad hoc force of local men who had formerly served in the Iraqi Army. The Fallujah Brigade failed dismally in this task, giving the insurgents another chance to claim victory and attract additional recruits. During the summer and autumn months, the Fallujah police turned a blind eye as the insurgents fortified positions inside Fallujah and stockpiled supplies. The Iraqi interim government, formed on June 28, 2004, then requested new efforts to capture and secure Fallujah.
The Americans initially labeled the assault Operation Phantom Fury. Iraqi prime minister Ayad Allawi, however, renamed it Al-Fajr (New Dawn). The operation's main objective was to demonstrate the ability of the Iraqi government to control its own territory, thereby bolstering its prestige. The American military focused on the importance of killing as many insurgents as possible while keeping coalition casualties low. About 10,000 American soldiers and marines and 2,000 Iraqi troops participated in Operation Al-Fajr. Some Royal Marines also took part. The American forces involved had considerable experience in urban combat.
taken from - Spencer C. Tucker et al., eds., The Encyclopedia of Middle East Wars: The United States in the Persian Gulf, Afghanistan, and Iraq Conflicts Volume II: E-L (Santa Barbara: ABC-CLIO, 2010), 441-442.