Files from 1996, released by the Public Record Office in Belfast, shed new light on the efforts of former Prime Minister John Major to persuade the Ulster Unionist Party (UUP) leader, David Trimble, to accept Senator George Mitchell as chair of all-party talks.
Mr Major also pushed the idea of parallel decommissioning of paramilitary weapons.
These issues and the likelihood of a renewed IRA ceasefire dominated a meeting which Mr Trimble and his UUP colleague, Reg [now Sir Reg] Empey had with Mr Major on 13 May 1996.
During the exchanges, Mr Trimble evinced deep suspicion of then SDLP leader John Hume, preferring to deal with the "straighter" Seamus Mallon.
The UUP leader opened by noting that the "IRA's American friends" appeared to be turning against them.The Good Friday Agreement - Ten chapters of the Troubles
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The prime minister agreed that this offered an important window of opportunity.
In his view, then-President Clinton clearly believed that his prospect of winning the US elections would be greater if there were an IRA ceasefire and progress in the talks.
Mr Trimble felt that if the IRA declared a new ceasefire, there would be pressure from the SDLP, the Irish and possibly the US to bring Sinn Féin into the talks.
"US pressure was on the IRA for now but… would then come on the unionists over decommissioning."
In these circumstances, Mr Major replied, the US would be heavily involved and the Clinton administration would want to see progress.
This meant that they would have to press for parallel decommissioning.
On the question of a talks chairman, the prime minister felt that having Senator Mitchell "in the hot seat" seemed the most attractive option.
The senator would be constrained by the need to be consistent with his own report - the "Mitchell Principles" on non-violence.
Mr Trimble said he had already written to President Clinton asking for assurances about Mr Mitchell.
He would need this before agreeing to a role for the envoy.
Mr Major suggested that the UUP leader should contact Mr Mitchell privately but Mr Empey detected "great suspicions within the UUP about the Americans", particularly around Nancy Soderberg who had previously supported a united Ireland.
Mr Major commented that there was no support for a united Ireland, north or south, and Mr Trimble agreed.
Mr Empey raised the possibility of Gerry Adams putting the Act of Union  on the table.
The prime minister agreed that he might do this but it was "only a fantasy item", undermined by the principle of consent.
The UK government's view, Mr Major stressed, could be deduced from its strong defence of the Union in Scotland.
However, Mr Trimble saw this as an unfortunate comparison.
The UK government seemed to wish to appear neutral about the status of Northern Ireland while defending the union strongly in Scotland and Wales.
The prime minister replied that the situations were very different: a violent campaign had been going on in Northern Ireland and the government had a responsibility to bring this to an end.
On a possible renewed IRA ceasefire, Mr Major commented: "If we manage the issues wisely, we could manoeuvre the IRA into a position where violence was no longer an option".
'Grappling with fog'
However, the then UUP leader believed that "the IRA would play it long and use the inevitably lengthy negotiations to their advantage".
For his part, Mr Empey felt that if Sinn Féin was not in the negotiations, John Hume would "hold the key".
Mr Major responded that Mr Hume would be under pressure from the Americans "who no longer took such a starry-eyed view" of the SDLP leader.
Mr Trimble said that Seamus Mallon's illness was unfortunate.
"His style was adversarial but at least straight. Dealing with Hume is like grappling with fog".
In attempting to sum up, Mr Major remarked that he and Mr Trimble were not far apart on the question of Senator Mitchell's involvement.
The UUP leader said that the shape of any North-South body and its status would be hugely important.
It was vital to get rid of the Anglo-Irish Agreement (signed by Margaret Thatcher and the then Taoiseach, Garret FitzGerald in 1985.).
In a note to Martin Howard, Patrick Mayhew's private secretary, afterwards, John Holmes, private secretary to the prime minister, struck a positive note: "The prime minister believes that Trimble is now close to accepting the role for Mitchell that the British government have in mind."
He confided that John Hume had rung Downing Street that day "asking why Trimble had had two meetings with the PM when he had not been able to get one".
He had managed to mollify the SDLP leader.