Will Gaddafi be allowed to go into internal exile?
As Nato's Libyan bombing campaign goes on, British officials are looking with increasing interest at a negotiated solution.
The key, they believe, may lie in gaining the acceptance of the National Transitional Council for a deal that allows Col Muammar Gaddafi to go into some form of internal exile once he has given up power.
When strikes began four months ago there was scant thought to how the campaign might end. Instead there was a sense of urgency about protecting the population of Benghazi, as tanks entered the city, and a desire to avoid a humanitarian disaster.
The ability to sustain the campaign is being tested now.
Although Liam Fox, the defence secretary, expressed his dismay earlier this week at those who questioned the ability to maintain the military pressure, it is evidently true that cuts in the Tornado force, which bears the brunt of British ground attack missions, would, if they go ahead, start to hamper that air campaign by late summer.
Of course, the Ministry of Defence will find work arounds if it has to, for example postponing cuts to the Tornado force. But that it finds itself in a position where it is cutting its aircraft and pilots at the same time that they are actively engaged in bombing another country is, I would think, historically without precedent.
Britain's problems are not unique. Several Nato countries engaged in the missions have started to run low on guided weapons, requiring the Americans to replenish them. The alliance realises that some lessening of military pressure is likely during Ramadan, which starts in one month.
They may chose, for example, not to bomb so many targets in built up areas during this time.
While the troika at the centre of this campaign - Britain, France, and the USA - have said that it will continue until Col Gaddafi is forced from power, many on the diplomatic and military side have despaired that the issuing of a war crimes warrant against him leaves the Libyan leader with no choice but to fight on 'like a cornered rat'.
In this regard too, the campaign does not seem have been the result of a joined up process, since these countries could have stopped the International Criminal Court from issuing this warrant. While war crimes charges might satisfy the demands for political pressure to be maintained, it can be argued that they will cost lives by prolonging the conflict.
So where does military fatigue and the difficulty of finding a way out for Col Gaddafi leave the campaign? Of course Nato leaders daily hope for a rising in Tripoli or that the colonel will be killed in one of their airstrikes. But since they insist they are not targeting him directly and his secret police apparatus still dominates the streets of the Libyan capital neither can be guaranteed.
In this tangled situation, statements by one or two senior figures on the revolutionary side that they might allow Gaddafi to go into internal exile as part of a process of transition have been received with the greatest interest. This offers a way out for everyone.
The problem though is that this 'solution' is highly suspect to many on the Transitional Council. They fear that if Gaddafi was hemmed into some desert compound, he could still exert his malign influence on Libya.
So while agreement eludes those who have tried to broker peace formulas, the business of negotiation grows daily more important.