When Germany surrendered in May 1945, the U.S. Army had more than 1.6 million men within the borders of the defeated Nazi state. Overnight they became occupation troops: Their orders were to spread out over every square mile of German territory and demonstrate without a doubt that they were in charge. U.S. troops secured every road junction, bridge, border post, government building, factory, bank, warehouse; anything of the slightest conceivable importance had a guard of GIs around it, and so did a good many things of little or no importance, too.

Army plans called for an occupation force of some 400,000 in the American zone for the first 18 months -- or one U.S. soldier for every 40 Germans.

When NATO forces went into Kosovo in 1999, they followed the same proven formula: 50,000 troops for a population of 2 million, one soldier for every 40 inhabitants. A recent Rand Corp. study by military analyst James Quinlivan concluded that the bare minimum ratio to provide security for the inhabitants of an occupied territory, let alone deal with an active insurgency, is one to 50.

In Iraq today, coalition forces number about 160,000, or one for every 160 Iraqis. (Even adding in an estimated 20,000 civilian security contractors working in Iraq, that still translates to one for every 140 Iraqis.) In response to the unremitting attacks and continuing instability, U.S. commanders have now canceled plans to cut troop strength by some 20,000 this year. It is a significant about-face, and one that has unquestionably put a severe strain on both regular and reserve units whose deployments have been extended well beyond what they had originally been told.

But it is still a drop in the bucket compared with what's needed. "U.S. Troop Levels in Iraq to Remain High," read a headline in The Washington Post this past week. Yet these levels are "high" relative only to the fantastically optimistic plans that the Defense Department had doggedly clung to as recently as a month ago.

The real tragedy of the current chaos in Iraq is that many military experts, historians and Army officials warned long before combat began that the projected number of postwar troops was utterly unrealistic. Army planners said they needed an initial occupation force of 250,000, which would still be half the number that the historically proven formula called for. Had they been listened to, and a robust force moved in at the start to establish firm control of the country and disarm the militias of political factions, it is possible that a rapid drawdown of U.S. forces could have followed, as civilian institutions began to function and life returned to normal in Iraq.

But those who called for a large force were not merely ignored; they were actually scorned. Both Defense Secretary Donald Rumsfeld and his deputy, Paul Wolfowitz, were furious when then-Army Chief of Staff Eric Shinseki told Congress that an initial force of several hundred thousand would be needed in postwar Iraq.

As many critics have since pointed out, Rumsfeld was apparently determined to make Iraq a showcase for the concepts of military "transformation" that he has championed -- the idea that given the vastly increased effectiveness of precision air power today, it is possible to fight with much smaller armies than was ever the case in the past.

It is important not to misread the lessons of the current manpower shortfall, however. Some critics of Rumsfeld & Co.'s pursuit of "war on the cheap" have suggested that the defense secretary was out to refute the "Powell doctrine," enunciated by Secretary of State Colin Powell when he was chairman of the Joint Chiefs of Staff. Powell maintained that when American military force is committed it should be "overwhelming" in order to ensure swift victory -- or, ideally, to convince an adversary that resistance is futile.

But, in fact, the American strategy pursued to defeat Saddam Hussein's army last year was pure Powell doctrine. The force was indeed overwhelming: It just did not take the conventional form of overwhelming numbers of tanks, artillery and foot soldiers with M-16s. Rumsfeld, and the Air Force, were supremely vindicated in proving the ability of a "transformational" American military to obliterate a conventional armored force in short order. Air power reduced entire armored divisions to a ragtag remnant of dismounted infantry. There were literally no more than a handful of occasions when an Iraqi tank was able even to attempt to fire at coalition forces. During the major combat operations, U.S. forces suffered fewer than 100 combat casualties.

What it takes to defeat an enemy army and what it takes to occupy and secure a country have never been exactly the same. But smart weapons and modern air power have created a startling disconnect between the two. The grave danger is that this has made it easier than ever to make the initial decision to use military force, while pushing off to the future the true costs in lives and troops and money -- costs that emerge only after the smoke has cleared and the battlefield is ours. Going to war used to be a step that America rightly approached with the greatest reluctance and gravity, given the far-from-certain outcome of any war (and the near-certainty of the huge sacrifice in human life that would ensue, even in victory). The effectiveness of modern American air power has now made victory as certain as it has ever been in the history of warfare; it has rendered the nightmare prospect of thousands, or hundreds of thousands, of battlefield deaths a bad memory from the seemingly distant past.

But it has made it no easier to deal with the consequences of victory. In Iraq, the Pentagon's real miscalculation was not that it believed that a ground force of such small size could defeat a well-armed enemy: It was to believe that the Iraqi people would so welcome us as liberators that no "occupation" would even be necessary.

The advocates of transformation are right in saying that we don't need huge World War II-style armies to win wars today. But we certainly need far more men and women on the ground than the current U.S. military can supply on its own, especially when we assume the burden of security and nation-building in a country whose government we have defeated on the battlefield.

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Stephen Budiansky is the author of "Air Power: The Men, Machines, and Ideas That Revolutionized War, From Kitty Hawk to Gulf War II" (Viking).