BAGHDAD — Next, we take on peanut butter.

One of the things I had the hardest time getting my head around before I left the states was whom, exactly, the U.S. is fighting in Iraq.

Turns out the answer is complicated enough to justify my confusion.

In Iraq, the military talks about two basic enemies, each, of course, with its own acronym -- AQI and JAM.

JAM, incidentally, is pronounced like the stuff you pair with peanut butter, because the military always likes to pronounce its acronyms even when that might lead to a certain amount of absurdity ("Be careful, sergeant, there's a lot of jam in this neighborhood!") The military embraces absurdity ... but I digress.

JAM stands for Jaesh al-Mahdi, which is Arabic for the Mahdi Army. The Mahdi Army, which originally referred to the militia controlled by radical Shiite cleric Moqtada al-Sadr, came to prominence when it staged an uprising against U.S. forces in 2004. After Sunni radicals bombed a Shiite holy place late that year, the Mahdis were at the forefront of a sectarian counteroffensive featuring death squads and block-by-block ethnic cleansing, which hurtled Iraq at least to the edge of civil war.

As the Mahdi prestige spread, its ranks swelled, at least in a manner of speaking. More and more militants held up the Mahdi banner, but it now seems clear that many were not answering to Sadr's organization. Real fault lines began to emerge after Sadr took steps toward a role in Iraqi politics this year and called for an end to militant activities by his followers. Many so-called Mahdi groups did not follow suit. Some may be influenced by ideology, although as The New York Times reported earlier this month, many of the groups more closely resemble criminal gangs grasping for some kind of legitimacy by holding to the Mahdi name.

So American commanders have gotten a lot more careful when they refer to JAM and now generally refer to the talk about the threat from "extremist elements of JAM." The military believes some of these elements are being armed by the Iranian regime, and most see a civil war between Sadr's followers and the Iranian-backed Shiite faction as a real possibility.

AQI, which stands for al-Qaida in Iraq, is the U.S.'s Sunni problem. Because of the way it operates -- as a group of loosely bound cells as opposed to a top-down organization -- it isn't easy to describe AQI in a few short sentences. Although Americans say AQI has ties to the international financing and training network whose name everyone learned six years ago, most members of AQI are seen as domestic insurgents, motivated at least as much by the humiliation of a foreign occupation and distrust of Iraq's Shiite majority as by the agenda of the hard-core jihadists..

As on the Shiite side, AQI's ranks grew and were in some cases unified by the sectarian fighting over the past few years. That is to say, at least, that the ranks of Sunni fighters the military classifies as AQI grew. Again, by no means are most of these seasoned mujahedin fighting since the Soviets invaded Afghanistan. But one of the real threats that's come out of Iraq is that the country will become a training ground for a new generation of jihadists, as Afghanistan was in the 1980s, and to some extent it already has.

But Iraq is, in many ways, a far different country than Afghanistan was, and AQI has far fewer and less powerful allies than that earlier generation of mujahedin, who could count the CIA among their helpers. The tribal sheiks in Anbar Province, the Iraqi Sunni heartland that a U.S. intelligence estimate deemed "lost" last year, have turned against the insurgents, and there have been a total of zero attacks on U.S. forces there this month. The unit I'm embedded with now fought a pitched battle through a Sunni enclave in Baghdad earlier this month, but here, too, the militants seem to have receded, and commanders say they're running out of neighborhoods to retreat to.

Yes, we've heard it before, but U.S. commanders in Iraq are genuinely optimistic. Their view, to paraphrase a little, is that Iraqis of both sects initially rejected the U.S. presence, at least in part because of heavy-handed American tactics, and entered a courtship with sectarian militias and civil war, which proved even more appalling, and now the U.S. has a second chance.