The BBC's Spotlight programme went to a number of people who have won the Nobel Peace Prize and asked them what effect the award had had on the process of winning agreement. F.W. de Klerk, the Afrikaner leader, probably put it best when he said: "It was inspirational and that was important, but in the end it was the tough, hard negotiations which secured a settlement."
All the former prize-winners spoke of their own experiences in a way which was startlingly relevant to the problems facing political leaders in Northern Ireland. The difficulties do not go away, a fact all too bitterly illustrated by the experience of those who had been involved in negotiations in the Middle East.
Shimon Peres, the Israeli Labour Party leader who shared the prize in 1994 with Yasser Arafat and Yitzhak Rabin, said: "It is not enough to negotiate with your enemy. You also have to negotiate with your own people and that can be the most difficult of all."
Hanan Ashrawi, one of the Palestinian negotiators who was standing in for Yasser Arafat on the programme, warned that the prize can be double-edged. At first it is seen as endorsing the efforts to reach a settlement, but if peace does not yield change on the streets, the disappointment, particularly among young people, will be all the greater and more dangerous.
There was the wisdom of real, hard experience here. It was F.W. de Klerk who said "You can never bring your entire power base with you because you cannot get everything they want". Peres added: "Do not lose heart if you cannot get everything that you want. Peace is the great disarmer."
Over and over again in recent days the questions that have been asked about last week's award of the Nobel Peace Prize to John Hume and David Trimble are: what effect will it have on the peace process in Northern Ireland? In particular, how will it influence David Trimble's ability to deal with the present difficulties, which he and Gerry Adams must face together, over decommissioning?
The important point to be made about the possible benign influence of the award was made by both David Trimble and John Hume when they heard the news. Each man emphasised that he regarded this as an award for the whole community in Northern Ireland.
This is not to detract in any way from the 30 years of absolute commitment to the search for peace which John Hume has given, or from David Trimble's political vision in recognising that the time had come for a historic accommodation between unionism and nationalism.
But as far as the effects of the Nobel Prize are concerned, this is also an endorsement of the courage shown by all those people who voted for the Belfast Agreement.
There were many people who had - and have - grave doubts as to whether the accord can deliver an inclusive and equitable settlement. That is as true of republicans as of unionists. Their instincts were to vote against it, but they put their worries and their narrow self-interest to one side and came out in support of dialogue and compromise.
This popular endorsement in the referendum, which was originally John Hume's idea, has been the crucial factor in maintaining the credibility of the peace process through the traumas of this past summer - Drumcree, the murder of the small Quinn boys and the Omagh bomb.
It was particularly important that the bravery of those in the broad unionist community who voted for change should be given international recognition. As John Taylor pointed out, unionism has never been accorded such political legitimacy on the international stage in the past. On the contrary, over the past 30 years, unionists have been held up to ridicule and worse as a collection of sectarian bigots, unwilling to live on terms of equality with their neighbours.
The comparison has often been made with the Afrikaners and Israelis, of a community determined to draw the wagons around the campfire and resist progress. Now, the award of the Nobel Prize to a unionist leader who has determined to lead his people forward to a more inclusive future must be seen as an encouragement for those who share his vision.
I hope this does not sound patronising. It is not meant to. The Nobel Prize will not help David Trimble with the dissidents within his own party, let alone his opponents outside it. But those who have been loyal both to the unionist leader and to the Belfast Agreement should see it as proper endorsement of the fortitude they have already demonstrated, and encouragement for the task still ahead.
FOR ALL these reasons, there is no doubt that it would have greatly helped Gerry Adams in his dealings with the IRA if his huge contribution to bringing peace had been given some similar recognition by the great and the good.
But the Sinn Fein leader was both wise and generous in his praise for both John Hume and David Trimble. Mr Adams knows that securing the settlement must be a co-operative project, and that whatever helps Mr Trimble at this moment should aid the process as a whole.
The current difficulty over decommissioning is one which Mr Trimble and Mr Adams have to solve together. There will be help, goodwill and advice available from outside, but ultimately these two political leaders will have to agree some formula which saves face all round, and then stand over it.
The conflicting views are clear enough. Sinn Fein points out that the text of the agreement is on its side and that there is no precondition for the hand-over of weapons prior to setting up the executive.
But, equally, the agreement demands that decommissioning should be completed within two years. This gives formidable moral force to the unionists' argument that they are entitled to know that concrete provisions will be put in place for this to happen.
It may be that what is finally agreed is a compromise formula which will be monitored by the endlessly patient Gen John de Chastelain. What must be remembered is that in this context the word "fudge" is not dishonourable. On the contrary, it is the very heart of negotiations of this kind. F.W. de Klerk has something to say on this. "If one side walks away with everything, then you have a victor and a vanquished, but you don't have a solution. You need a solution in order to secure the settlement."