BAGHDAD – As violence diminishes and U.S. troops draw down, Iraqis are trying to figure out what kind of political system will emerge when American influence fades.

The nature of that system matters to Americans, too. The purpose of Gen. David Petraeus' "surge" strategy was to stabilize Iraq so it would no longer provide a haven for al-Qaida or a fertile field for Iranian intervention. But Iraq's political system is increasingly fragmented.

Although Shiites and Sunnis are no longer fighting, there are growing splits within those sects and tensions between Kurds and Arabs. Many Iraqis yearn for another strongman – a "good Saddam." Some think Prime Minister Nouri al-Maliki wants that title.

So is some form of democracy really possible in Iraq? Will the country pull together or splinter? After two weeks of talking to leaders of all factions, I've found some grounds for optimism, despite huge obstacles ahead.

First, some history: After the Iraq invasion, U.S. officials set up a political system dominated by religious and ethnic parties, led by returning exiles. Secular parties were marginalized. Many middle-class Iraqis who opposed religion-based politics fled abroad.

As Iraq heads into a year of provincial and national elections, Iraqis tell me they are tired of religious parties. "Something called Iraqi nationalism has re-emerged," said Mowaffak al-Rubaie, national security adviser to Maliki. "Something called Iraqi-ism has re-emerged." But can that re-emergent sense of Iraqi-ness help knit the country back together? Or will it feed into the yearning for a "good Saddam"?

Maliki has played on the growing yearning for Iraqi unity. By cracking down on Shiite militias in the south, even though he is a Shiite, and by accusing Kurds of expansionism, he has won support from many Sunni Arabs, who now view him as a champion of a centralized Iraq.

Others accuse Maliki of dictatorial intent – of meddling with the military and maintaining an intelligence service with links to Iran. "Unfortunately, Maliki is a ruler, not a leader," said Qassim Daoud, an independent Shiite parliamentarian. Recently, Maliki ordered the arrest of dozens of officials in the Ministry of Interior, initially claiming a coup threat. Many saw the move as a warning to would-be competitors.

But this prime minister can't become a dictator. His Dawa party holds only nine parliamentary seats, and the Iraqi army won't subvert the constitution, especially with U.S. troops in the country.

Moreover, tribal leaders tell me that Maliki's controversial efforts to organize support groups among Shiite tribes are unlikely to win serious voter support.

And Maliki quickly released the arrested Ministry of Interior officials, probably because he got so much criticism from the media and other political parties.

The more crucial question is whether the new sense of Iraqi-ness can keep the country from fragmenting. I saw signs that politicians from major parties were aware that the country was yearning for stability, not political brawls.

One sign: Shiite, Sunni and Kurdish parties that discussed bringing Maliki down via a no-confidence vote have put such ideas on hold. "A vote of no confidence is not on the agenda," I was told by Vice President Adel Abdul Mahdi, a leader of the Islamic Supreme Council of Iraq, the largest Shiite party. "We have taken into account the fragility of the country's situation, and public opinion."

Another sign: Parties that pushed for strong federal regions – which some see as a prelude to soft partition – have toned down their demands. The Islamic Supreme Council of Iraq is not pushing its proposal for a nine-province region in the Shiite south, and it pooh-poohs efforts by the oil-rich Basra province to become a region on its own.

A third sign: The Kurds have agreed to postpone a referendum on the explosive issue of whether oil-rich Kirkuk should be joined with their federal region. Iraqi President Jalal Talabani, a Kurd, traveled to Kirkuk to reassure nervous Arabs, Turkmen and Christians of Kurds' peaceful intent.

A fourth sign: Sunni Arabs, who refused to participate in previous elections, are forming new parties and gearing up for the vote.

In short, despite the tense atmosphere in Iraq, jaw-jaw seems to be replacing war-war. "People got fed up from the killing, assassinations, bombs and explosives," Daoud said. "There will be clashes and temporary crises," Mahdi said, "but no civil war."

All sides tell me they want to create alliances across Shiite, Sunni and Kurdish lines. So do leaders of Shiite and Sunni tribes that are running candidates for the first time in the Jan. 31 provincial elections. But past politics in Iraq were a zero-sum game; it may be hard now to grasp the meaning of power-sharing.

"Dialogue does not mean that people are willing to compromise," one savvy Iraqi politician told me. "But no one is thinking of going to the streets." That, at least, is progress of a kind that no one dreamed of 18 months ago.

Reach Trudy Rubin at trubin@phillynews.com.