I’ve always rejected comparisons between the Iraq war and World War II because they are so misleading.

Yet when people ask me whether this week’s Iraq elections are a turning point that may enable U.S. troops to draw down, I find myself quoting Winston Churchill. “This is not the end,” Churchill said, following Montgomery’s victory at El Alamein in November 1942. “It is not even the beginning of the end. But it is, perhaps, the end of the beginning.”

The Iraqi elections offer a hope that the conflict may begin to shift from the era of car bombs into an era where violence is undercut by politics.

Previous elections didn’t stem the bloodshed because they failed to address the problem that underlies the violence. The alienated Sunni minority, which ruled Iraq under Saddam and produces most of the insurgents, felt it had no role in the new Iraq. Sunnis refused to take part in legislative elections in January. But this time Sunnis crammed the polls, even in violent towns like Ramadi where the insurgency is potent.

Two factors led to this Sunni attitude change.

First, many Sunnis realized the boycott shut them out of a political process in which Kurds and Shiites were divvying up Iraq’s riches. In July, when I was in Baghdad, Sunni intellectuals and clerics told me their boycott had been mistaken. New election laws, which assured the Sunnis of more seats, helped persuade them to vote.

Second, U.S. policy toward the Sunni minority has undergone a sea change. Under U.S. occupation czar Paul Bremer in 2003-2004, there was no “Sunni strategy.” Bremer dismissed the Iraqi army, propelling many Sunni officers into insurgent ranks; he endorsed a broad de-Baathification purge that left even mid-level members of Saddam’s political party with no hope of work.

When I visited Ramadi in 2003, well-known Sunni tribal sheikhs told me they had been willing to work with the Americans, but instead U.S. soldiers had raided their houses. Probably, some of those same tribesmen went on to support insurgents who lay the IEDs that blow up U.S. troops.

But U.S. Ambassador Zalmay Khalilzad, who arrived in July, has been actively engaging Sunni leaders in hopes of undercutting the insurgents. He displays diplomatic skills that have been sorely lacking until now.

There are some hopeful signs. In Ramadi, Sunni tribal guards – not U.S. or Iraqi soldiers – protected the polling places. This is a critical shift, since Iraq’s new army still has few Sunni troops.

Another hopeful sign: Insurgent groups like the Islamic Army of Iraq told their fighters not to attack polling stations (though they urged Iraqis to keep killing U.S. soldiers). Even al-Qaida, which denounced the elections, didn’t threaten to disrupt them.

In other words, the different insurgent factions, both Iraqi and foreign Arabs, understood they could not flaunt the public will.

So Iraq has reached the end of the beginning phase of post-Saddam life, where Sunnis chose to resist only with the gun. But will this lead to a phase where Iraqis can settle their differences in parliament and American troops can leave?

Not clear. At present, many educated Sunnis still believe – falsely – that they are a numerical majority. The elections will produce a Sunni bloc of about 20 percent in the national assembly. Can Sunnis come to grips with their reduced role?

Moreover, the reason so many Sunnis voted is because they want to resolve huge grievances. They fear the dominant Shiite and Kurdish parties will split Iraq into pieces. Iraq’s new constitution permits Kurdish and Shiite provinces to join into super-regions and control the rich, unexplored oil fields in the north and south.

If the new Iraqi government addresses these concerns, it is possible that Sunni leaders, including tribal sheikhs, may take a stronger stand against parts of the insurgency, especially the Arab jihadis who are blowing up Shiite markets and mosques. Then Shiite, Kurdish and Sunni leaders could work together on another key Sunni demand: a timetable for U.S. troop withdrawal.

But this all depends on untested new leaders with little experience of compromise. It also depends on Khalilzad’s skills and a whole lot of luck.

Iraq’s new parliament could deadlock, its leaders unable to keep the country from splitting. Or new Sunni leaders could, like Northern Ireland’s Sinn Fein, provide a front for continued violence by IRA-style guerrillas.

The Iraqi elections have offered hope but no guarantees. They are the end of the beginning. Now we have entered a new phase whose outlines will only become clear in the next few months.