American policy in Iraq is heavily influenced by the 1990s peacekeeping experience in the Balkans. Bosnia, in particular, has many parallels with Iraq. Bosnia was also dominated by religious and ethnic differences. Nearly all of the 4.2 million people there were Slavs, but 44 percent were Moslems (Christians who converted during centuries of Turkish rule), 31 percent were Serbs (Orthodox Christians who use the Russian alphabet) and 17 percent Croats (Roman Catholics who use the Roman alphabet). The other eight percent considered themselves "Yugoslavs" or something else (Albanians, Turks, and so on). The Bosnian Serbs and Croats had military and financial support from larger kinsmen in adjacent Serbia (to the east) and Croatia (to the west.) After four years of fighting, and over 300,000 dead, a peace deal was imposed. But the three groups were allowed to retain control of their own territory, governments and armies. Actually, the Serbs were the most independent, and also protected the largest number of prominent war criminals. Now, after eight years, of NATO occupation, the factions of Bosnia are armed, dangerous and ready to resume fighting. Once a civil war begins, the hatreds and resentments linger for a long time.
In Iraq, it was decided that factions would not be allowed to form militias and separate governments. This would help prevent a civil war. The biggest problem here was that the Kurds had already formed two governments (based on two major Kurd factions) during the 1990s, when American and British air power kept Saddam's troops and police out of northern Iraq. Since last May, much diplomatic effort has gone into getting the Kurds to disarm and go along with a new national Iraqi government. You don't hear much about this, because it was in everyone's interest to make the Kurds look united and willing to be a part of Iraq. Neither condition is entirely true, but Kurds are, at the moment, more interested in peace and prosperity than nationalism and revenge.
Shia attempts to form militias have been met with forceful prohibitions against that sort of thing. Sunni Arabs have been subject to numerous raids to remove weapons and ammunition. The Iraqi army was disbanded right after the war because it was known that it's officers had been selected mainly for their loyalty to Saddam. Most of the officers were also Sunni Arabs. Leaving the army intact would have created a Sunni Arab militia, a large body of armed men resentful of the American presence in the country. Although many of the troops were Shia Arabs, they were terrorized and dominated by Sunni officers and NCOs. If the Iraqi army were left intact, the Sunni officers would have to deal with unrest in the ranks as well as devising ways to continue the fight against the Americans.
Another lesson learned was to restore law and order before holding elections. In Bosnia, elections were held quickly, and the warlords became the elected leaders. Corruption thus insured that billions of dollars in foreign aid got stolen, criminals run much of the economy and ethnic tensions remain high. By letting things calm down before holding elections, there will be time for a better class of political leaders to arise. Electing the guy with the most gunmen or deepest pockets does not work very well.