Even by Baghdad standards, Thursday's bombings were shocking. Mayhem in the Parliament building and the disabling of a key bridge over the Tigris River illustrated the dim prospect of a purely military solution to Iraq's civil war.

　　 Earlier in the week, a peaceful event delivered an equally potent message. Tens of thousands of Iraqis turned out Monday in the Shiite holy city of Najaf to protest the U.S. occupation. As the Bush administration's continual floundering in Iraq ought to make clear, policymakers must seek to understand the motives of key players in Iraqi politics.

　　 The Najaf demonstration was above all a show of influence by the demagogic young cleric Moktada al-Sadr.

　　 Just before the Najaf event U.S. forces clashed with some of Sadr's militia, who call themselves the Mahdi Army, in Diwaniya, a town near Baghdad. One signal sent by the crowds in Najaf was that the Americans should not push too hard against the Mahdi Army.

　　 Sadr's lieutenants pointedly boasted that his militia has grown at least threefold since being routed by the Americans in Najaf in 2004. By including a smattering of Sunni Arab clerics and even some Kurds in Monday's demonstration, and by stressing a nationalist rather than a sectarian theme, Sadr was warning the Americans that a serious attack on his forces would be tantamount to attacking all patriotic Iraqis who were happy to be free of Saddam Hussei's dictatorship.

　　 Sadr, whom senior ayatollahs have scorned as an unlearned hothead, was also sending a message to the Shiite clerical establishment that he is too powerful to be ignored. By making a show of his mass base and his Iranian backing, Sadr is seeking to be recognized as first among his peers.

　　 Sadr's street theater in Najaf offers a lesson for U.S. policymakers: a tolerable exit from Iraq will require that they learn to play the complex, many-sided game of Iraqi politics.