From the American point of view, the ideal outcome is one that produces low casualties, drives Saddam out of power and leaves Iraq in one piece, able to defend itself but not strong enough to threaten its neighbors. Any such result would also achieve the official U.S. objective: to get Iraq out of Kuwait. Freeing Kuwait, however, is only part of a complicated process that is full of pitfalls for the allies. “The question isn’t whether we’re going to win,” says a Pentagon official. “The question is how we win, and what options that leaves us with afterward.” Although analysts disagree on the nuances, there are several ways in which the conflict might end:

Before the land war begins - or even a week or two into the campaign - the Iraqi dictator could call the whole thing off, ordering his troops home. That would be a high-risk ploy. Saddam would fail in his principal objective, the absorption of Kuwait, and would be left with no tangible payoff for the losses he has suffered so far in the air war. He might be overthrown by his own generals or advisers. But even in retreat, Saddam’s stature in the Arab world could be enormously enhanced if he is seen as the man who stood up to America, Israel and the rest of the West and managed to lash back by firing Scud missiles into Israel and Saudi Arabia and sending his troops to attack the Saudi town of Khafji.

“Saddam has pushed aside any number of lifelines, but I think this scenario is a fair possibility,” Richard Murphy, the assistant secretary of state for Mideast affairs in the Reagan administration, said last week. “Saddam has lasted a full three weeks, and that’s three times as long as Syria, Jordan and Egypt lasted in 1967. " If Saddam pulls out before the land war gets rolling, a large part of his Army would remain intact. So would much of his Air Force, assuming Iran gives back the 147 warplanes that have taken sanctuary there. With such means of intimidation left, he might be able to regain at the negotiating table some of what he gave up in leaving Kuwait: the oilfield and islands he covets.

For the United States, such an outcome would give Bush a victory in Kuwait with a minimum of bloodshed. But it could leave Saddam in power and would certainly deprive Bush of the chance to completely destroy Iraq’s military machine. Some U.S. officials describe an early end to the war as the “nightmare scenario.” If Saddam attempts it, the allies will try to keep him from withdrawing his armor, according to a senior official who is familiar with Bush’s thinking on the subject. Bush’s men calculate they would have a week or so to bomb Iraqi forces and knock out the river bridges that heavy equipment would need for a retreat.

But once Saddam begins to meet Bush’s demand for “a credible, visible withdrawal,” the Americans would have to let up and allow his troops - if not their tanks - to escape. U.S. officials don’t think it will come to that. “There will be a window of opportunity for him,” says one, “after he’s bloodied us but before his military apparatus is decimated, to revert to his pragmatist, survivor mode. But he’s very likely to ignore it or miss it. He is a brinksman who doesn’t know where the brink is, and his ego may well have become too grandiose for him to do this.”

This is a more likely outcome. Saddam is nothing without his Army; if he loses it, he could forfeit his rule or his life. But if he can put up a good fight for a month or two, he might be able to survive an outright defeat. The Republican Guards, the largest body of troops on which his regime depends, are deployed in northern Kuwait and southern Iraq. If he throws in the towel at the right moment, he might be able to extricate many of them from a battlefield disaster.

In this outcome, Saddam would be a hero to much of the Arab world and would continue to pose at least a political threat to his neighbors. But symbolism can cut both ways. With Saddam still in power, it would be relatively easy to hold the anti-Saddam coalition together, at least for a while. If Saddam hangs on, the Bush administration will try to maintain an embargo on Iraqi oil exports and military purchases, sources say. The sanctions would break down eventually, but the goal would be to weaken Saddam as much as possible in the hope that he would be overthrown.

The United States might also be tempted to keep a military presence in Saudi Arabia. “In the long run, that would work against us,” says Gregory Gause, a Mideast expert at Columbia University. “It would be harder to come to a security understanding with the Iranians. And the presence of large-scale American forces in Saudi Arabia in the medium term would serve as a focal point for discontent there.”

His downfall is the other most likely outcome, and even if it occurs late in the conflict, it would be a blessing for Washington. With Saddam out of the way, it might well be easier to make peace, perhaps using the services of mediators like Iran, the Soviet Union or Algeria. In a post-Saddam climate, the allies would have the opportunity to create a new security structure in the gulf region, to promote arms control and, further afield, even to tackle the Palestinian problem.

Saddam would probably be replaced by someone much like himself - a member of the political inner circle of relatives and yes men or a general who has survived the dictator’s periodic purges of the military. A respectable general would be the best of the feasible successors. Fred Halliday, a Mideast expert at the London School of Economics, calls this “the Badoglio solution,” referring to the field marshal who replaced Mussolini and paved the way for Italy’s surrender in World War II. “It’s the real Arab solution - a nationalist military coup in Baghdad,” says Halliday. “It lets everyone off the hook. Effectively, it undoes the 2nd of August” - the Iraqi invasion of Kuwait. Even if some thoroughly despicable figure takes power, he almost cannot help but be an improvement over Saddam, from the allied point of view. “There are problems with a post-Saddam Iraq, but they’re not nearly as great as the problems of Iraq with Saddam,” says Gause. “It’s easier to deal with a dead martyr than a live hero.”

The danger is that post-Saddam Iraq could simply collapse. Any new government might be too weak to oppose the separatist impulses of the rebellious Kurdish minority or the downtrodden Shiite majority. Ambitious neighbors such as Iran or Syria would be tempted to snatch pieces of territory for themselves, Balkanizing Iraq and plunging the region into a new spasm of instability, with disastrous consequences for countries like Jordan.

Although U.S. officials consider this to be the least likely result, Saddam might be able to resist for longer than expected, for any of a number of reasons: good Iraqi morale, bad weather, the failure of high-tech U.S. weapons, the use of Iraqi poison gas, or a split in the anti-Saddam coalition, perhaps caused by Israel being dragged into the war. The conflict also could be prolonged if allied objectives change, requiring a deeper ground thrust into Iraq than now planned.

A longer war would hurt the United States at home, straining the economy and exacerbating racial tensions because of the disproportionate number of blacks in the front lines. If the allies try to end the war by lunging toward Baghdad, the war could turn bloodier and uglier. The invaders would run into populated areas and religious sites that would be hotly defended by soldiers and civilians alike. An invasion of Iraq would arouse anti-American sentiment throughout the Arab world, where people are linked by strong ties of religion and culture. “These connections are not evident to generals, who see only military targets, and President Bush doesn’t see them,” says Edward Said, a literature.professor at Columbia University and an independent member of the Palestine National Council, the PLO’s parliament in exile. “He is like Captain Ahab looking at Moby Dick,” charges Said. “He’s completely obsessed with Saddam Hussein.”

Administration officials insist they are not after Saddam personally, if only because he is too elusive a target. They also say the United States does not want to destroy Iraq or occupy it. And they are confident that the allied attack will not get bogged down. “Once we start advancing, [Saddam’s] troops will have a choice: they can stay in their bunkers and be mowed down, or they can come out to fight and be chewed up by our combination of air and ground power,” says a senior U.S. official.

In all the endgame scenarios, however, the most important variable is what happens to Saddam Hussein. If he remains in power, both the war and its aftermath will be more difficult. But defeat in war could discredit both Saddam and his regime, leading to his political or physical demise. In that case, says one U.S. official, “the new regime might be unstable. The Iraqis will hate us. But Iraq will be whole. Its regime will be more pragmatic. And we can deal with that.” The key element in resolving a complicated struggle thus becomes a simple question of one man’s survival.