With almost a week now over since the start of the operations in Afghanistan, the US military is predictably claiming success. Circumspection is always the best approach in dealing with such claims, partly because boasts about heavy damage are a key instrument in a wider propaganda effort, and partly because the process of damage assessment - undertaken after each air or missile strike - is fairly subjective. Most of the wars over the last decade have been confrontations between vastly unequal antagonists, with the weaker party - be it the Yugoslav military or the Taliban in Afghanistan - resorting to decoys and deception as a key defence strategy.
Military installations and training camps have been flattened. But, as the US military itself admits, considerable doubt must remain about how significant these hits are for the operational capabilities of the Taliban and the terrorist organisations it is shielding. All that can be said at this stage is that military experience suggests that damage assessments from previous conflicts have been persistently over-optimistic.
It is clear that US military planners were not only concerned with destroying the Taliban and the terrorists. They were also keen to manage the inflated expectations of American public opinion about how quickly a military operation can produce decisive results, while nurturing the coalition of countries supporting the current operations at the same time. The snag for Washington is that these aims may be inherently incompatible. And for President Bush, the real challenges are only just beginning.
The first week of the operations was deceptively reminiscent of the war against Iraq a decade ago: swift strikes to disable air defences, followed by more persistent raids against military installations. But in reality, the aims of the current war are radically different.
A decade ago Washington sought to evict invading Iraqi forces from Kuwait, not to topple the Iraqi regime; this time, the overthrow of the Taliban remains the primary objective, a necessary first step before the introduction of small detachments of ground forces, tasked with the elimination of terrorist hideouts.
The problem for the military planners is that although there is little doubt that the Taliban regime will collapse, this has to happen fairly quickly. The reason for the rush is not military, but US public opinion.
Until now, the US did a good job in managing public expectations at home. Instead of shooting from the hip immediately after the terrorist atrocities, it patiently built up its forces in Central Asia and carefully mapped out its strategy.
Meanwhile, every Administration official claims that the war should be measured in months or even years. And the President has been careful not to portray bin Laden himself as the primary objective; indeed, the name of this terrorist was not even mentioned in Mr Bush's first address to his nation as the operations began.
Public support for the President remains very high; most ordinary Americans understand the inherent difficulties of the operation, and the sheer impossibility of eliminating every terrorist overnight. But the reality remains that, while previous air campaigns in which the US was involved shored up support for a president, this air campaign, if continued for much longer, will actually infuriate American public opinion.
Throughout the last decade some Americans doubted the wisdom of engaging in wars in Iraq or the Balkans, and many more did not want any US casualties. The lengthy air bombardment of Iraq or Yugoslavia therefore came as a relief, an indication that Washington was sparing no effort to minimise US troop casualties.
But matters are different this time, because this war is regarded as protecting the US itself. Therefore, there is a limit to how many contrived daily press conferences broadcast live from the Pentagon ordinary Americans would stomach.
Nor are Americans likely to be amused if they continue to be presented every night with the same grainy, barely visible pictures purporting to show a few mud huts destroyed in Afghanistan.
If the operation does not shift its tempo pretty soon, public opinion will start asking searching question about the entire scope of the mission, and Bush's abilities to manage the military effort.
The Administration can claim as often as it wishes that the war would be long and hard, and it can refer to as many UN Security Council resolutions as it wants; none of this will wash with a public which expects retribution and decisive action.
The Pentagon is evidently hoping for a swift collapse of the Taliban regime. This would not only be touted as a first and reassuring success for US public opinion, but would also be the sign for a series of surgical ground attacks against terrorist targets.
The distinction between air and ground offensives will become increasingly blurred; both will take place simultaneously in various locations.
Military planners are only too aware of the fact that at least some of the ground operations may result in the capture of nothing more than an abandoned training camp or cave.
They are also aware that the Taliban may lose control over Afghanistan's biggest cities, but still exercise sway in the countryside. This should not matter, provided that at least some of the operations score a direct hit and that the area in which terrorists can hide is progressively reduced.
The onset of winter and the start of the Ramadan holy month should not present insurmountable difficulties either. In fact, heat-seeking infrared equipment may be more potent in identifying hidden groups of individuals during winter, and the Koran has no interdiction against fighting during Ramadan: Iran, Iraq and the various Afghan guerrillas continued fighting during this Muslim holy month for years. In short, the operation can continue for months; only its pace and character need to change soon. However, managing the alliance of countries supporting this operation is guaranteed to get trickier. World-wide Muslim backlash against the US is, paradoxically, not the most pressing problem.
The demonstrations in Pakistan are still confined to small political groups, and their importance may have been magnified by an international media corps which sits in Pakistan with precious little else to report. The key to power in Pakistan remains the military, and this is still under Gen Musharraf's control. Matters will change if the US allows the imposition of a government formed exclusively by the Northern Alliance of rebels, widely regarded in Pakistan as Moscow's stooges.
Partly in order to prevent this from happening, the US actually refrained from bombing some Taliban troop concentrations this week, in order to slow down a potential Northern Alliance offensive towards Kabul.
But these Taliban forces are now being targeted, and the US is involved here in a delicate balancing act, which requires the removal of the Taliban as quickly as possible in order to satisfy US public opinion, but not before a broad-based Afghan alternative government, which must include elements sympathetic to Pakistan, is formed.
And behind the scenes, promises are being made to various governments. The Russians evidently hope that their proxies will emerge victorious; the Pakistanis are told that their allies will also be part of the government. And the Israelis are promised continued support, while the Palestinians are told that their dream of an independent state is not far off.
Current talk about widening the war to other countries is no more than noise, a tussle inside the Administration between hardliners eager to hit at Iraq and moderates who wish to confine the war to Afghanistan. The moderates are winning, if only because the international coalition is sure to collapse if an attack on Iraq takes place. And, strange as it may seem, the fuzziness of Washington's stated war aims does allow the US quite a lot of room for manoeuvre. But the options are narrowing fast. Very soon, President Bush will have to answer all the questions his military planners avoided so skilfully this week: his public at home will demand to see results, while his allies abroad would wish to know what kind of Afghanistan the US is proposing to construct for the future.
Jonathan Eyal is director of studies at the Royal United Services Institute in London