WASHINGTON — The first big test of security gains linked to the U.S. troop buildup in Iraq is at hand.

The military has started to reverse the 30,000-strong troop increase and commanders are hoping the drop in insurgent and sectarian violence in recent months — achieved at the cost of hundreds of lives — won’t prove fleeting.

The current total of 20 combat brigades is shrinking to 19 as the 3rd Brigade, 1st Cavalry Division, operating in volatile Diyala province, leaves. The U.S. command in Baghdad announced on Saturday that the brigade had begun heading home to Fort Hood, Texas, and that its battle space will be taken by another brigade already operating in Iraq.

Between January and July — on a schedule not yet made public — the force is to shrink further to 15 brigades. The total number of U.S. troops will likely go from 167,000 now to 140,000 to 145,000 by July, six months before President Bush leaves office and a new commander in chief enters the White House.

As the U.S. troop reductions proceed, it should become clear whether the so-called “surge” strategy that increased the U.S. troop presence in and around Baghdad resulted in any lasting gains against sectarianism. Critics note that the divided government in Baghdad has made few, if any, strides toward political reconciliation that the Americans have 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 war began in 2003, 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 since it started.

A key question is whether security will slip once U.S. lines thin and whether Gen. David Petraeus, the top U.S. commander in Iraq and orchestrator of 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 that 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 now rather than from big, isolated U.S. bases. Living among the Iraqis, they say, allows for a building of greater trust.

That trust, in turn, prompted more local Iraqis — mostly Sunni Arabs but also 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 in uncovering roadside bombs before they detonate.

The commander of U.S. forces in Baghdad, Maj. Gen. Joseph Fil of the 1st Cavalry Division, told reporters Nov. 6 that it was too early to declare victory over al-Qaida in Iraq, the mainly Iraqi terrorist organization that has been a chief target of U.S. offensive operations in recent months.

But Fil said it was now clear that U.S. forces, with Iraqi help, have gained the upper hand in Baghdad.

“Perhaps even most significantly, the Iraqi people have just decided they’ve had it up to here with violence,” he said.