WHAT an odd way to run a war. Nearly a week into the allied air operations in Libya, the command structure remains murky. True, the coalition headed by America, France and Britain had to act in haste, and has had to build a command structure on the fly.

So after much intense diplomacy, NATO has agreed to take over the running of the no-fly zone over Libya. Yet the coalition will remain in charge of operations to attack Libyan forces on the ground. “At this moment, there will still be a coalition operation and a NATO operation,” said Anders Fogh Rasmussen, the NATO secretary-general.

This hybrid arrangement may be necessary to hold together those who are more muscular in terms of attacking Libyan forces on the ground, and those who want to stick to patrolling the airspace and waters. But it could prove awkward over time. It is reminiscent of the unhappy command-and-control arrangement that lasted for years in Afghanistan, whereby the NATO-led ISAF mission was responsible for peacekeeping and stabilisation while, alongside it, an American-led coalition ran the counter-terrorist mission, known as Operation Enduring Freedom (OEF).

This was often an uncomfortable arrangement, causing much resentment, as special forces would sometimes hit targets without informing NATO commanders supposedly in charge of a particular area of operations. European commanders complained privately about gung-ho Americans while Americans seethed about spineless Europeans. Eventually the matter was resolved. America boosted its forces and took overall command of ISAF, bringing OEF under a single commander.

The situation may not be as bad in Libya; NATO and the current coalition may be a distinction without a difference. The NATO commander who will be in charge of the no-fly zone, Admiral Samuel Locklear, is the same naval officer who, with an American hat, is already running the coalition's Operation Odyssey Dawn. Moreover, the British say they expect all aspects of the operation to come under NATO command in the coming days.

The debate about the degree to which NATO controls the operation is odd. For the Americans, bringing NATO in means handing over responsibility to Europeans; for Europeans, NATO means America. France has resisted giving NATO too prominent a role for fear that it will turn off Arab allies; Italy says the NATO label would be an attraction because it would put a straitjacket on the gung-ho French.

While military commanders are accustomed to operating with different NATO and national hats, the politics may not be resolved until one of two things happens: either the coalition stops hitting ground targets to make the operation more palatable to Turkey, or Turkey accepts that bombing tanks and artillery firing on Libyan towns is, in fact, a necessary part of protecting civilians.

This leads back to the uncomfortable questions that have dogged the intervention: what are the aims and limits of the operation? And how long will it go on for? Speaking at a summit of European leaders in Brussels, President Nicolas Sarkozy of France said last night the coalition had stopped a repetition of the Srebrenica massacre in 1995. That alone justifies taking action, but it does not answer how the operation will end.

As matters stand, the coalition has resorted to enough force to stop Colonel Qaddafi from crushing the revolt, but not yet enough to remove him from power. At this intensity, the intervention may well lead to a frozen conflict: think of Iraq under sanctions, no-fly zones and occasional air strikes for 12 years. The trouble with such a prospect is that Colonel Qaddafi could simply outlast the coalition's will to continue policing Libya; as with Iraq, sanctions have a tendency over time to weaken those imposing them.

Kurt Volker, a former American ambassador to NATO, offers a maximalist interpretation of the UN resolution authorising the use of force to protect Libyan civilians. “The sooner the West adopts a clear position that the UN's humanitarian goals can only be achieved by Qaddafi's removal from power, the sooner the crisis can begin to come to an end.”

Nobody is yet prepared to adopt such a position. Indeed, President Sarkozy last night offered a more limited set of objectives. The video of his press conference is here. To sum up, he said the coalition's job was to protect civilians from the threat of attack. Removing Colonel Qaddafi was a job for Libyans themselves. His condition for ending the attacks was for Libyan forces to withdraw to barracks and to stop besieging Libyan towns, not the departure of the colonel.

He offered a reason for sticking to a fairly narrow interpretation of the resolution: the need to maintain Arab support. As well as a couple of Qatari planes, the UAE has now confirmed it will send 12 jets to help out. Their rules of engagement are unclear. But all this is precious help, politically if not militarily.

In one of his more thoughtful moments, Mr Sarkozy said the prize was not just the fate of the Libyan people, but winning back the trust of Arab people as they seek to free themselves of autocratic rulers. He told Syria and Yemen, among others, that he will maintain the same position: Europeans would stand on the side of peaceful demonstrators against those who fire on their own people.

One can argue that Mr Sarkozy's formulation does not resolve the underlying worries about a stalemate. If Colonel Qaddafi really stopped resorting to force he would be finished anyway. So one should not expect him to stop entirely, though he might change tactics—for example putting his forces inside towns rather than around them to make it harder to hit them without causing civilian casualties. The French high command is already giving notice that operations could go on for weeks rather than days. It may be much longer.

One hope is that the regime will break up internally. Hillary Clinton has spoken of senior regime figures putting out feelers about possible exile, and Mr Sarkozy publicly encouraged defections, saying those who dissociated themselves from Colonel Qaddafi would have a place in a future Libya. David Cameron, the British prime minister, warned regime loyalists that every day they continued to support Colonel Qaddafi would bring them closer to prosecution for war crimes in the Internatiional Criminal Court. He told them:

Don't obey his orders. Walk away from your tanks. Leave the command-and-control that you are doing. Give up on this regime because it should be over for him and his henchmen.

But given the experience of Iraq, it is hard to put much faith in this outcome; Saddam was only removed by a full-blown invasion.

Can one increase pressure on the colonel to hasten his demise? French officials are speaking of creating large zones of humanitarian protections, defended by the United Nations. Another is to move beyond merely protecting Mr Qaddafi's opponents to strengthening them: beginning with humanitarian aid, and perhaps increasing the rebels' political profile (France would like the oppostion "national council" in Benghazi to be represented at next week's conference on Libya in London). Should one train and arm them too? “It is a good question,” says one senior French source, nodding his head.

One problem with this strategy is that there is currently an arms embargo on Libya. A new UN resolution would be needed, and one could expect intense resistance to the notion of the world arming one side of a civil war. The danger is of arming the wrong sort of people—the opposition national council includes prominent former members of Colonel Qaddafi's regime. Another risk is of a future“blowback” of the sort that took place in Afghanistan, where some of the anti-Soviet Arab fighters that were supported by the West and Saudi Arabia in the 1980s went on to become the core of al-Qaeda.

Mr Sarkozy said the decision to take action in Libya was hard to take. Deciding how to end it may prove even more difficult.