NOT FOR A generation have Americans had to consider the most somber question that can face a nation on the brink of war: if the shooting starts, what kind of war do we want to fight?

Conflict with Iraq is not inevitable, yet this issue is squarely before us now. The 19th-century German military strategist Karl von Clausewitz tells us that we have two fundamental choices. We can fight a war that seeks to overthrow the enemy. Or we can fight a war that seeks more limited objectives, such as restoration of the status quo.

At stake are tens of thousands of potential casualties, a hemorrhage of national wealth at an estimated $1 billion a day, and the risk of fighting, in Gen. Omar Bradley's ominous phrase of 40 years ago, "the wrong war, at the wrong place, at the wrong time, and with the wrong enemy."

Publicly, President Bush speaks of restoring Kuwait's sovereignty and preventing Iraq from swallowing Saudi Arabia. This suggests, if negotiation fails, a limited conflict.

But privately, the U.S. government recognizes that a satisfactory, enduring solution to the current crisis is impossible without basic changes in a Baghdad regime that now possesses huge stocks of chemical weapons and would like to own nuclear bombs. "We can take Saddam Hussein without a million-man army, or a million man army without Saddam Hussein," a House Armed Services Committee staff member said last week. "But we can't take both of them, because Iraq's ability to intimidate will remain." Thus, within a few days of the invasion, Bush ordered the government to begin planning an effort to destablize and eventually remove Saddam from power.

This goal suggests, that unless Saddam is assassinated, overthrown, or chooses early retirement, the United States will fight a war to topple him.

In pursuit of that end, we again have two fundamental choices: we can fight a war of annihilation, a term of art that does not imply wanton slaughter but rather the obliteration of an enemy's military power. Or we can fight a war of attrition, indirectly bending the enemy to our will by exhausting him.

For most of our history, as the respected military historian Russell F. Weigley documents, we have fought wars of annihilation, notably the Civil War and the world wars. Until 1962, the Army field manual contained this unambiguous statement: "The ultimate objective of all military operations is the destruction of the enemy's armed forces and his will to fight." Douglas MacArthur said it more succinctly: "There is no substitute for victory." Americans possess "a profound distaste for the very notion of containment and limited war," political scientist Robert E. Osgood once wrote, an aversion aggravated by stalemate in Korea and defeat in Vietnam.

Bush seems to be preparing the nation to fight a war of annihilation and has upped the ante as high as it will go: "Our jobs, our way of life, our own freedom and the freedom of friendly countries around the world would all suffer if control of the world's great oil reserves fell into the hands of Saddam Hussein." By repeatedly drawing an analogy between Saddam and Hitler, the president has invoked both the moral warrant of World War II and the strategic concept of total war.

Thus far, however, the U.S. approach suggests a strategy of attrition, even if the present confrontation turns bloody. Although the Iraqi government yesterday described the current embargo as "an act of war," U.S. forces and their allies are arrayed defensively and remain relatively modest by the standards of 20th century juggernauts. Iraq is encircled, more or less, yet not threatened with imminent attack; with 160,000 Iraqi troops in Kuwait, many military analysts believe a force of 300,000 to 500,000 would be necessary to dislodge the invaders.

"You do have a kind of disjuncture between the intent of getting rid of Saddam Hussein and the methods that seem to be politically feasible to go about doing it," Weigley said last week. "I doubt that many people have thought it through yet and you can't exactly blame them. The action was cobbled together quickly and only now is there leisure to think about the implications . . . . We're in a kind of quandary, where our means and ends don't match up with each other."

The principal American weapon for the moment is the blockade. As a senior House staff member summarized the approach: "You strangle Iraq and present its army with a choice -- either get rid of Saddam or see your country crumble."

Embargo-and-blockade is a tactic as old as siege warfare; the current approach is similar to the "Anaconda" plan adopted by the Union to encoil and squeeze the Confederacy. Sometimes it works, often it does not. The South ultimately was crushed only through a brutal war of annihilation. Iraq reportedly has several months of wheat and rice reserves, which can be stretched in a national emergency and augmented by smuggling -- particularly if Iran accepts Saddam's peace overture.

Of course the current attrition strategy may be an interim approach, a stopgap until all diplomatic efforts have been exhausted and a critical mass of soldiers, warplanes, ships and tanks is assembled to wage a war of annihilation. Bush decided Friday to begin activating the reserves, and the forces now coiling in the Saudi desert have an incresingly offensive look. It's hard to foresee the precise trigger that would push today's stalemate into tomorrow's war, particularly since Saddam seems to have concluded that time and impasse are his allies; regardless of who fires the first shot, the quick, forceful strike envisioned by American war-fighting doctrine seems likely, particularly to destroy pre-emptively Iraqi chemical weapons and anti-aircraft systems. In selecting either a strategy of annihilation or attrition, the United States would choose between two distinct sets of advantages and perils.

In our wars of annihilation, historically we have been "accustomed to victory wrought with the weight of materiel and population brought to bear," as an authoritative Army document noted in 1976. The United States has 15 times the population of Iraq, 80 times the gross national product and, to date, a globe full of allies. The end of the Cold War removes the principal impediment that prevented the United States from waging wars of annihilation in Korea and Vietnam -- the fear of triggering Soviet intervention and perhaps nuclear war.

All-out war also plays to the traditional "offensive spirit" of the American armed forces, a state of mind derived from Napoleon -- who powerfully influenced the developing U.S. military -- and cultivated ever since. As the 1982 Army field manual declares, "Destruction of the opposing force is achieved by throwing the enemy off balance with powerful initial blows from unexpected directions and then following up rapidly to prevent his recovery. Our operations must be rapid, unpredictable, violent and disorienting."

Moreover, 40 years of preparing for Armageddon against the Soviet Union would serve U.S. forces well against Iraq, military theorists believe. "Ironically, we've been practicing to fight exactly the right enemy," said Harry G. Summers Jr., an historian and retired Army colonel. Although the Iraqi arsenal is heavily stocked with French and Chinese weaponry, for the most part Baghdad "uses Soviet doctrine and Soviet equipment," Summers added. Like their former Soviet patrons, for example, the Iraqis tend to attack in echelons -- waves -- and to mass their artillery. "We have a very solid doctrine," said Brig. Gen. Timothy J. Grogan, deputy chief of staff at the U.S. Training and Doctrine Command. "For the kind of warfighting we would do against a major opponent, the Iraqis or other Soviet-style {enemy}, we're in good shape."

But conflict -- particularly a desperate war of annihilation -- is unpredictable. "When war comes," an American admiral once observed, "we at once move into a radically different world." In trying to outmuscle a weaker foe, the Soviet Union had similiar advantages in population and economic strength -- and much shorter supply lines -- when it invaded Afghanistan in 1979.

If the fear of a superpower clash is gone, other obstacles give pause to anyone pondering full-bore war against Iraq, including the potential enmity of other Arab states and the endangerment of perhaps 3 million expatriate hostages. "And the last two big wars, Korea and Vietnam, created a new constraint in the United States," Weigley added, "the fear of the political unpopularity of any prolonged military involvement."

Finally, given the arsenals available in 1990, a war of annihilation would be annihilative indeed. Since the Yom Kippur War, when Israel, Egypt and Syria lost a combined 2,800 tanks and 614 warplanes in two weeks, military analysts have recognized a "new lethality" wrought by computer-guided "smart" munitions and other modern weapons. An American tank in World War II had to fire 13 rounds for a 50 percent probability of hitting a stationary tank a mile away; by the mid-1970s, that PK -- probability of kill -- ratio had improved to one round. Even total victory in Iraq could be horribly Pyrrhic, destroying much of the exceptional U.S. force built by Ronald Reagan's $2 trillion investment. Astrategy of attrition has its own allure. Iraqi military targets are vulnerable to U.S. air superiority, so Bush could cross the threshhold from economic to military war without waging a huge ground conflict. By controlling the tempo of the war, he could perhaps wear down Iraq without incurring staggering U.S. losses. And a war of attrition probably would not require a resumption of the draft, though almost certainly it would entail extensive support by the National Guard and Reserves, which, since Vietnam, have been woven deliberately and deeply into the force structure.

But wars of attrition also are perilous. As Defense Secretary Dick Cheney said Friday,"I do not know when we will be able to come home." That bodes poorly for a nation of impatient temperament.

"After the experiences of Indochina," Weigley wrote in "The American Way of War," "the idea that the United States can work its will in distant parts of the world by means of the measured, controlled application of punitive violence seems especially dubious."

The benefits of air supremacy, for example, often have been exaggerated. In North Korea, U.S. bombing reduced the two main rail systems to roughly one-tenth of their pre-war capacity, yet the communists continued to carry half of their armies' required tonnage by rail. North Vietnam successfully endured precision and saturation bombing that lasted for years. Ousting 160,000 Iraqi troops from Kuwait -- to make good on Bush's pledge that the invasion "will not stand" -- probably would require a substantial ground force to augment Air Force and Navy bombing.

And a slow squeezing by the United States of Iraq -- rather than a direct commitment to crush the enemy -- risks forfeiting what Clausewitz called "the strength of passions" of a people mobilized for war. That is precisely what happened, as Summers has written, in the Vietnam War.

In looking to the past for guidance in the future, certain lessons suggest themselves. For one, the articulate assertion of unambiguous national goals is critical in harnessing not only the nation but also the military; a 1974 survey of generals who had commanded in Vietnam found that almost 70 percent were uncertain of their objectives.

If Bush opts for total war, he is gambling that he has correctly gauged the mettle of America. To seek an enemy's overthrow, Clausewitz wrote, is to "presuppose a great physical or moral superiority, or a great spirit of enterprise, an innate propensity to extreme hazards." Is that the America of 1990?

The choices before the nation are difficult and dangerous, the consequences impossible to anticipate. Reviewing the four variables cited by Omar Bradley in his "wrong war, wrong place, wrong time, wrong enemy" equation, the statistical probabilities of fighting a wholly righteous conflict are remote. It is our common concern to determine whether we face the right war, in the right place, at the right time, with the right enemy.

Staff researcher Lucy Shackelford contributed to this article.

Rick Atkinson is a member of the investigative staff of The Washington Post.