WASHINGTON PUNDITS are focused on the difficult challenge of winning the hearts and minds of the Arab world. We would be well advised to spend some time thinking about how to win some hearts and minds in Europe.

The situation in Britain is not as favorable as one might think if you looked only at the polls. Sure, Prime Minister Blair's approval rating is strong, fully recovered from the pounding he was receiving in the months leading up to the war. A large majority (65 percent) recognize that the war is going well and have adjusted their expectations to a war measured in months rather than weeks. And a reassuringly tiny percentage, 9 percent, think that the U.S. military is taking too few precautions to avoid civilian casualties.

Such robust support is remarkable, given the largely negative coverage the war has received in the media. The liberal papers are unabashedly antiwar and the conservative papers, with the exception of the tabloid Sun, are surprisingly guarded. The vaunted BBC's coverage was so slanted that its senior defense correspondent actually filed an internal memo complaining about it.

The media are always careful to report favorably on the activities of the British troops per se, but these are usually framed with a negative spin that puts U.S. forces in an especially negative light--British troops adapting well to the failures of the American plan, British troops facing serious friendly-fire threat from cowboy American pilots, British troops abandoned by American forces who survive ordeal. That sort of thing.

Part of this is simply the latest installment in the mixture of admiration and envy that has characterized Anglo-American military relations for decades. A senior retired general relayed to me numerous stories from World War II, and then launched into his own detailed explanation on how British troops today were much less prone to error than American troops.

Stacked against Blair's rock-solid support, these are minor annoyances. But they point to a deeper problem in the coalition: Apart from Blair and a handful of the most knowledgeable experts, relatively few elites support the coalition because they are convinced it was wise or necessary to confront Hussein with force. What support exists is more conditional and resigned--Better to follow the United States than France, but our boys are going to get whacked for it.

This means that setbacks are felt more acutely in Britain, and some, like the friendly fire incidents, receive an extraordinary amount of attention. The war is described as more of a near-run thing than it is in U.S. media. One classic example: a page one, above-the-fold, breathless description of a tank firefight by an embedded Times reporter. He described the exposed isolation of the lads--where was that promised American air cover?--and declared his own survival a matter of luck. As an aside, he noted that no British tanks were hit, no British soldiers killed, apparently not even any wounds suffered. All Iraqi tanks were destroyed. A rout was described as if it were Gallipoli.

Despite a steady diet of this sort of thing, support among the general public is strong. But, as Desi Arnaz would have said, the United States will have some explaining to do if the Brits suffer any serious setbacks. Fortunately, the British sector appears to be calming down and they are not likely to join the battle for Baghdad itself.

On the continent, the battle for the hearts and minds has hardly begun, and this will make repairing the transatlantic breach very difficult. The war is stunningly unpopular in Spain, despite the government's steady support. In Germany, the foreign policy elite is nervous about the damage done to transatlantic comity and is already maneuvering to repair U.S.-German relations. Just yesterday, the German government made explicit its hope that the United States would quickly defeat Iraq; true, not quite enough to be counted among the coalition of the willing, but a symbolic gesture nonetheless.