Both the British and Irish governments now see a way to convene round- table discussions by working out a programme for decommissioning of terrorist weapons in parallel with, rather than before, the talks.
Political sources on the British side said last week that an "unequivocal commitment" by the IRA never to use arms again may be enough to initiate the early stages of the all-party talks. A firm statement of intent along these lines would be "something we can run with".
This is something the Ulster Unionists are likely to oppose, but one suggestion is that they may be persuaded to accept it if there is also a commitment to convene an elected assembly, something which they have been demanding.
Officials are optimistic that a formula of this kind can keep the peace process moving forward and maintain the momentum created by President Bill Clinton's successful visit to Ireland last week.
Under the plan, weapons would be handed in once talks had begun, in accordance with a timetable laid down by the international commission set up last week to investigate the issue. This body will be chaired by a former US senator, George Mitchell, sitting with a Finn and a Canadian.
Acceptance of parallel decommissioning would represent a concession from Britain's so-called "Washington Three" condition, laid down by Sir Patrick Mayhew, Secretary of State for Northern Ireland. But the Prime Minister has already given some hints of flexibility over this. In the Commons last week, he described the Washington Three condition as "not a matter of dogma; it is a matter of practicality. It goes without saying that we, like the Irish government, will consider constructively any practical suggestions that could help bring all parties into negotiations on the basis of the Downing Street declaration."
That leaves open the way for alternative possibilities and for progress, if they can create the confidence required to get the Unionists into all- party talks.
One source on the British side played down the Unionist veto. "Hitherto, the Unionists could come to the table and walk away if they didn't like it. They refused to accept an agenda 'dictated by terrorism'. That option is not available to them in the same way."
Yesterday Labour's Northern Ireland spokeswoman, Marjorie Mowlam, appeared to boost the idea of a new assembly when she suggested new elections for parties wanting to join all-party talks. She told Channel 4's A Week in Politics: "I think there is a way through which says that if we are looking for a mechanism that gets everybody into all-party talks, we could have a kind of election passport that says, participate in the election and then it is into negotiations.
"I think it is a possibility that I know some of the parties in Northern Ireland are looking at."
Sinn Fein has yet to commit itself to the twin-track process or talk in detail about the hand-over of weapons. But it will be under acute pressure to co-operate with the Mitchell Commission, which is expected to begin its work this week and report to London and Dublin before the end of January.
Neither government will give evidence, but both are likely to be given advance warning of its findings. Its recommendations on whether the paramilitaries have a will and an intention to get rid of their arms, and if so, how it could be done, will be advisory.
But British sources said ministers "may be faced with a situation where there is something less than the letter of Washington Three, but which could be bloody difficult, politically, not to take notice of".
The Rev Ian Paisley, leader of the Democratic Unionist Party, has reacted angrily to the first moves towards fresh talks. On Friday the British and Irish governments issued identical letters of invitation to all the parties, including Sinn Fein, and Mr Paisley declared that his party would not respond. It was an insult, he added, that the invitations had been issued by both governments, and he accused the British Government of abandoning its role as the sovereign power and giving Dublin joint management and control.