From the start, the war in the Gulf was a race against casualties: an effort to bomb Saddam Hussein into submission before TV pictures of the carnage killed popular support for the war. But it was American casualties -- the specter of thousands of body bags containing dead GIs -- that the administration was worried about. Few suspected that it would be dead Iraqis -- and mere scores rather than thousands -- that would trigger the first massive revulsion over the war.

It's too soon to know the immediate toll of the U.S. bombing of that air-raid shelter in Baghdad, let alone the long-term political damage, caused by the raid. Convincing evidence that the shelter also served as a military command-and-control center (as allied authorities insist), or that the Iraqis deliberately used their own innocent civilians as protective cover for their military operations, could help to transform potential political catastrophe into mere calamity. Allied failure to disprove Iraqi claims that the shelter was only a shelter might prove ruinous to the American will.

Presumably we'll know more about that later. What is interesting now is how little it has taken to shake our confidence in our ability to avoid large-scale "collateral damage." Only two bombs fell on that heavily reinforced building, and early Iraqi accounts put the deaths at fewer than 65. (The numbers have since climbed).

Nor has there been any evidence to counter our confidence in the precision of war technology. One Iraqi account made the stealth assault seem almost uncannily precise: the first bomb, according to that account, was placed so as to seal off the exits so that the second could wreak its carnage.

No, what has been called into question is not the accuracy of our munitions but the reliability of our vaunted military intelligence. Our military people claim to have called the strike only after they had amassed irrefutable evidence that the building was a communications center and that at least from time to time it housed high-ranking Iraqi brass. But what they showed us were sketches, not reconnaissance photographs of the building's supposed military use. They told us of intercepted communications proving their claim that the Iraqis were directing their war from the building, but they produced none of the communications -- ostensibly because it would let the enemy know what frequencies we are tapping and what codes we have broken. They have provided few answers to some of the more obvious questions: for instance, how were they able to observe the communications equipment being brought into the building, or the military brass arriving in their limousines, and still be completely unaware that the building was being used routinely as an air raid shelter for civilians?

Even so, few Americans (though apparently a good many Iraqis and Iraqi sympathizers) doubt that the allies have been at great pains to avoid killing civilians. And as far as I know, Wednesday's disaster may leave support for the war largely intact.

But only if there is no repetition. Many more pictures of dead children, of destroyed homes and schools -- of "collateral damage" -- could bring popular pressure for a quick end to the fighting.

Bush may want no more Vietnams, but the people want no more My Lais -- no more slaughter, intended or not, of noncombatants. As Associated Press correspondent Mike Feinsilber put it, "The country wants a clean war." Indeed you could plot public support of war, even before the bombing started, by asking Americans to predict the number of American casualties. Those who thought the number would be fewer than 3,000 favored the war; those who thought the number would be higher tended to oppose it.

But there are no clean wars, not when the public gets its reports not days after the fact, as in World War II, but daily -- often hourly. And with TV pictures, not sanitized newsreels.

The generals know that as well as you, and the safest bet is that they'll return to their relatively sanitary attacks on indisputably military targets and start looking -- finally -- for a way out of the war. A few more mistakes like Wednesday's, and we might wind up bombing ourselves into submission.