Scenario One: Iraqi stability unravels over the next year, overwhelming the government's 600,000 soldiers and cops. Scenario Two: Iraqi stability maintains its not-great-but-not-awful levels, and those soldiers and cops continue to need logistical and support aid. Does keeping 50,000 U.S. troops in Iraq make sense in either scenario?

In the first case, 50,000 soldiers - troops that mostly stay on their bases - aren't going to be enough to beat back a revived insurgency. In the second, 50,000 troops seems like way too many for a training mission. That's why strategists are having a hard time finding the military logic behind a force that's simultaneously too large and too small.

It's not clear how rapidly the U.S. will pull those troops out of Iraq ahead of the full December 2011 withdrawal. But for the time being, "in terms of a purely train-and-advise [mission] for a military that's got its feet on ground, it does seem to be a whole lot," says Steven Metz of the U.S. Army War College.

Adds retired Major General Paul Eaton, who served in Iraq during the war's early years, "50,000 is a nice round number, and it's attractive to [use] 50,000 simply for that reason." Surprise, surprise: the U.S.' continued involvement in Middle Eastern politics does more to explain the current force size than military necessity.

An undisclosed number of Special Operations Forces are staying in Iraq to hunt terrorists. But for the most part, seven Army brigades comprise the U.S.'s remaining force in Iraq: the First, Second, Third and Fourth Brigades of the 3rd Infantry Division; the First Brigade, 1st Armored Division; the Second Brigade, 25th Infantry Division; and the Fourth Brigade, 4th Infantry Division. They've been re-purposed into a new and unfamiliar formation called "Advisory and Assistance Brigades."

What's that mean for their ability to engage in combat if things start going badly? Colonel Thomas Collins, an Army spokesman, says we should consider about two-thirds of the troops to be trigger-pullers, with the rest serving as headquarters staff, logistics and other functions. (Though everyone in uniform carries a weapon, of course.)

That's a high proportion of shooters. Usually, notes the Council on Foreign Relations' Steve Biddle, a brigade deployed to a war zone consists of about half combat troops and half support troops. And it's especially surprising since the troops aren't supposed to be engaging in combat, after all. But the figure highlights what Biddle calls the "tremendous amount of ambiguity in these missions."

An example: for years, training the Iraqi security forces involved bringing them along on U.S. combat operations. But as the Iraqis gotten better, training is less intense. U.S. trainers now focus largely on helping the Iraqis master their logistics, maintain their equipment and bolster their intelligence capabilities. "In terms of actual combat units - shooters - the need for American trainers and advisers is minimal," Metz assesses.

According to Collins, the number of troops ready to prevent Iraq from unraveling is closer to 33,000. But even if the unraveling occurs, expect that force to take a back seat to the Iraqi soldiers and police, who have been protecting Iraq's cities since last June. U.S. troops are "not going back to leading a counterinsurgency again," Metz assesses. Nor is there any appetite in the Obama administration for re-surging troops to Iraq, as a top White House adviser indicated to Danger Room on Tuesday - something that would probably be necessary if the Iraqis are overwhelmed by a revived insurgency. If it took 150,000 troops years to tamp down the insurgency, 33,000 troops - a figure on its way down to zero - don't stand much of a chance.

"To be perfectly honest," Biddle says, "I think the most important function the troops are serving is more psychological than technically, concretely military."

That is, they're there in that number as a political reassurance to Iraqi Sunnis and Kurds that the Shiite majority isn't going to go all Saddam Hussein on them. Even if the U.S. isn't visible on the streets of Iraqi cities anymore, their nearby presence helps steady Iraq's shaky post-civil war political balance. It's like the NATO peacekeeping role in the Balkans, Biddle contends, allowing "the parties to become accustomed to living together without having their minds focused on the moment of [U.S.] withdrawal." (That's why Biddle says he's increasingly worried about the full U.S. pullout next year.)

Peter Mansoor, a former brigade commander in Iraq who served as General Petraeus's executive officer during the troop surge, agrees that peacekeeping is the real mission of the residual force, even if the Obama administration and the generals don't put it that way. "The most important, albeit unstated, function of the U.S. forces remaining behind is not to advise and train security forces, but to serve as honest brokers to keep the peace between the various Iraqi sects and factions," says Mansoor, who now teaches military history at the Ohio State University. "The number of troops currently in Iraq is adequate for this purpose."

Metz adds another point. Those 50,000 troops are a check on additional regional meddling in Iraq. The Iraqi military is built around light and mobile forces that can provide internal defense against insurgents. It doesn't have a large armored corps or a mature air force that can deter an invasion, especially from traditional rival (turned quasi-sponsor) Iran.

For the next year-plus, U.S. troops are a "tripwire, as much of a symbol of commitment as anything," Metz says. "We do not have the numbers there to actually fight off an invasion, but it's enough that the U.S. is committed" to deter one.

For the last seven years, at every stage of the Iraq war, troop levels looked woefully insufficient to some military analysts and provocatively large to others. Who would have thought that both critiques would apply simultaneously as the war enters its terminal phase?