Few of Mr Shea's media counterparts are so diligent. When the lights go down for the 3pm press conference in the cavernous Joseph Luns lecture theatre at Nato headquarters, the audience is noticeably thinning.
Even in peacetime, Nato is a bizarre institution, housed in a converted maternity hospital in an anonymous suburb near Brussels airport. It has a barber, travel agent and a Royal Mail postbox, but Russian is one of the most common languages in the press room.
Yet with the air campaign in its third month, Nato's media war has settled into a rut, if a rather surreal one. Each day there is a list of targets blasted at unpronounceable locations and video images of imploding buildings. But the statistics of death and destruction have lost their power to shock, and less and less of the output of Nato's briefings seem to enter the public domain.
In the huge, windowless canteen, Tony Blair's press secretary, Alastair Campbell, appears regularly and seems in ebullient form, but even he is finding this war a difficult one to spin. The abiding image of the campaign to much of the public is one of Nato bungling and civilian death, rather than Serbian butchery in Kosovo.
For the alliance, the problems arise at several levels. The most obvious difficulty is that Nato is often reacting to news rather than making it. Belgrade's formidable propaganda machine controls the TV pictures which emerge from Serbia and Kosovo. Inevitably these are of Nato's mistakes, the destroyed civilian buildings and mangled tractors (some of which may not, in fact, have been destroyed by Nato bombs). The Serbian media can get their version of events out at a time when Nato's cumbersome military bureaucracy has little idea of what has happened and its spokesman are stalling. Yet, propaganda or not, Belgrade's accounts have proved close to the truth often enough to make them impossible to ignore.
At a political level, Nato headquarters faces a constant battle to present the alliance as a united force in the face of clear and deep divisions over the possible deployment of ground troops. An early visit by Mr Blair to Brussels was judged a big success, with positive coverage, but in attempting to repeat that performance Nato shot itself spectacularly in the foot.
When, two weeks ago, Robin Cook, the Foreign Secretary, Gerhard Schroder, the German Chancellor, and Massimo D'Alema, the Italian Prime Minister, visited Nato on successive days, each gave a different message. This is just a taste of the divisions that will emerge if the alliance has to contemplate fighting its way into Kosovo.
Nato's beefed-up media team has, however, been fighting back, particularly with the all-important TV networks who have been invited on visits to military bases in Italy with General Wesley Clark, supreme allied commander. For the first time the Ministry of Defence's nuclear bunker in London was filmed, the pictures being used on the day of the relaunch of the BBC's 9pm news.
More difficult has been the task of re-focusing the attention of the media on the reasons for the war and combating what Mr Blair describes as "refugee fatigue". With the bombing in its third month, the plight of the populace of Kosovo, camping in appalling conditions in Macedonia and Albania, has become one of the established facts of the war, rather than news. Frustrated at the media's failure to concentrate on the causes of the war, Mr Shea's language has got steadily more polemic.
On one occasion he began quoting from Macbeth as he described Serbian attempts to conceal evidence of war crimes: "Out damned spot, out I say," quoth Mr Shea to a surprised press. "Here's the smell of blood still. All the perfumes of Arabia will not sweeten this little hand. What's done cannot be undone."
More serious have been the factual errors which have undermined the media operation. Early in the campaign Nato announced that three prominent ethnic Albanians were thought to have been murdered by Serb forces, only to have to admit later that they were alive. When one of them, Fehmi Agani, was killed weeks later, the news got only limited coverage. Partly as a result of this episode, when Nato pointed to signs of civilian unrest inside Serbia, it was initially treated with great caution by the world's media.
The alliance's media difficulties also reflect its military failings. For weeks the daily brief- ings failed to give any significant information about the damage done to Serbian forces in Kosovo, reinforcing the idea that this was an air war being waged against civilian targets in Serbia proper. In fact the alliance was concentrating more and more on Serbian armed units in Kosovo, but was just not having much success. Only in the past three weeks have Nato pilots succeeded in hitting military targets in any significant numbers. Although more than 60 per cent of Serb tanks, heavy artillery and armoured personnel carriers remain intact, the alliance is now making slow but steady progress.
Over the last week the perverse momentum of the media war has started to move in Nato's direction. Familiarity with the air campaign has begun to drive it off the top of news bulletins and newspaper front pages. Last week saw a sustained period without a big bombing error and, because of the scale of Nato's earlier mistakes, smaller incidents of "collateral damage", such as an attack on a prison at Istok, cause less public outrage. The macabre joke is that, after hitting the Chinese embassy and a hospital, Nato will have to bomb an orphanage before the world takes notice.
At the outset of the air war one of Nato's top media strategists likened the conflict to a political election campaign, and argued that the Western media were worth 20 points to Slobodan Milosevic. Nine weeks on the gap is closing. Boredom may be the alliance's secret weapon.
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