The first of five U.S. combat brigades scheduled to leave Iraq by next summer has begun heading home to Fort Hood, Texas.

The return of the 3rd Brigade, 1st Cavalry Division — currently operating in the Diyala province — is the beginning of the force adjustments that are part of the troop drawdown that President Bush announced in September following a highly anticipated report by Gen. David Petraeus and Ambassador Ryan Crocker.

At the time Bush said he would bring combat levels down from 20 brigades to 15 by summer 2008, with the first of those brigades coming home by the end of this year. The troop reductions are expected to be about 30,000 — the amount boosted earlier this year by Bush's troop-surge plan, with an expected troop level of 140,000-145,000 by July.

Pentagon Spokesman Bryan Whitman said Tuesday that although one brigade is redeploying, the number of brigades in Iraq will not be reduced to 19 until January because other units will be coming in before then.

The U.S. command in Baghdad announced Saturday that the Fort Hood-based brigade had begun heading home.

Whitman also said commanders on the ground in Iraq make decisions to backfill for forces leaving, depending on the security situation. Therefore, it is more than likely other forces in Iraq will be shifted to the Diyala once this brigade is out.

As the U.S. troop reductions proceed, it should become clear whether the "surge" strategy that increased the U.S. troop presence in and around Baghdad resulted in any lasting gains.

Critics note the divided government in Baghdad has made few, if any, strides toward political reconciliation, which Washington has said is crucial to stabilizing the country.

The acceleration of the U.S. mission away from direct combat to more of a support role will put greater pressure on Iraqi security forces to bear more of the load. And it will test the durability of new U.S. alliances with neighborhood watch groups springing up with surprising speed.

Declines in Iraqi civilian and U.S. military casualties in the past few months and talk among U.S. commanders of an emerging air of optimism and civic revival in some Baghdad neighborhoods point to positive security trends.

Although more U.S. troops have died in Iraq this year — at least 856 — than in any year since the 2003 U.S. invasion, the monthly count has declined substantially since summer. Iraqi civilian deaths also have declined. At least 3,861 Americans have died in the Iraq war.

A key question is whether security will slip once U.S. lines thin and whether Petraeus, who orchestrated the counterinsurgency strategy, has made enough inroads against insurgents — and instilled enough hope in ordinary Iraqis — to make the gains stick.

U.S. commanders assert it is not just the larger number of U.S. troops that has made a difference but also the way those troops operate — closer to the Iraqi population rather than from big, isolated U.S. bases. Living among the Iraqis, they say, allows trust to develop.

That trust, in turn, has prompted more local Iraqis — mostly Sunni Arabs, but also some Shiites—to join U.S. forces in anti-insurgent alliances, the commanders say. It also has meant more Iraqi help in finding insurgents' arms caches, reducing mortar attacks and uncovering roadside bombs before they detonate.

Stephen Biddle of the Council on Foreign Relations, who has assessed the situation for Petraeus, said a key reason for recent security gains is the emergence of the local anti-insurgent alliances—not just in Anbar province where they began early this year but also now in and around Baghdad. A key to sustaining those security gains will be the U.S. military's ability to police those alliances, he said.

"It's happening on a large-scale basis throughout much of the country," Biddle said. "The problem is how do you keep them from either [switching] sides again or from going to war against each other."

Brig. Gen. Stephen Gledhill, the second-in-command for training Iraqi forces, says he is confident that conditions have improved to the point where the Iraqis are capable of filling any U.S. gaps. "Our answer is that they not only will be able to—they already are and will continue to do so as they gain experience, capabilities and capacity," he said.

FOX News' Justin Fishel and Jennifer Griffin and The Associated Press contributed to this report.