COMMENTARY: The presidential presence brings its own magic of course. This historic occasion in Northern Ireland was also enhanced by good news from the war front and (it seems) rising expectations of a successful conclusion to the peace process at home.
Even so, it was possible to marvel at the contrast between the man and the caricature - he of the notoriously mangled syntax waxing lyrical about constructing a settlement in the Middle East and nothing short of an Arab democracy in Iraq.
In a remarkable role reversal, President Bush came to mock the cynics. "I believe there's some scepticism in Europe as to whether I mean what I say. Saddam Hussein knows I mean what I say. The people of Iraq know I mean what I say," he rebuked. They needed to keep on hearing it: "We will not stop until they are free. Saddam Hussein will be gone." And thereafter? "I hear a lot of talk about how we are going to impose a leader. Forget it," he instructed. The allies would remain until the Iraqi people themselves were ready to run their own country. "That's precisely what's going to happen," he promised.
It was a cynical world which said the Iraqis could not govern themselves. They were "plenty able to" the president declared. Not much hint there of the American imperialism feared by the British left and in much of Europe. Mr Bush confirmed he and Mr Blair were agreed the UN had a "vital role" to play in the reconstruction of Iraq. They would seek a new UN resolution affirming Iraq's territorial integrity, ensuring rapid delivery of humanitarian relief and endorsement of an appropriate post-conflict administration.
Labour opponents of Mr Blair's alliance with the Republican president would have been quick to spot the potential get-out clause. What would "endorsement" amount to? Who would decide what was "appropriate"? The ambiguity would remain. Yet Mr Bush went further than London might have hoped. He welcomed UN Secretary General Kofi Annan's appointment of a special adviser for Iraq to work with the Iraqi people and coalition representatives.
And he allowed that the UN could help identify people to serve on the proposed multi-ethnic Interim Iraqi Authority (IIA) which America and the UK intend should precede elections and the emergence of a representative government.
The scale of this ambition was writ large in yesterday's joint statement, which again appeared to carry a powerful message for those who fear this president has no interest in "nation building" and sees the conflict in Iraq as the prelude to military action elsewhere.
As they had said in the Azores, Mr Bush and Mr Blair yesterday affirmed: "We will uphold our responsibility to help the people of Iraq build a nation that is whole, free and at peace with itself and its neighbours." Downing Street was delighted.
While the precise mechanism for determining the composition of the IIA had yet to be decided, Mr Blair's official spokesman said the principle had been established that the UN was part of "the consensus-building process."
Mr Blair underlined his practical and pragmatic approach to achieving that consensus, insisting there was "no reason to go back" to the dispute over a second UN resolution authorising the war.
Pressed about the role of the UN, Mr Blair said: "The important thing is not to get into some battle about words on the precise role here or there." For the coalition and the international community the priority should be to focus on the needs of the Iraqi people and the expression of their will through institutions that they in the end would own. The prime minister and his advisers were also delighted by the development of the President Bush's vision for the Middle East. Mr Blair's spokesman said this had "validated" the choice of Hillsborough as the venue for the summit.
Two 45-minute walks in the gardens, it seemed, had helped Mr Blair impress on Mr Bush the potential - borne out by the Northern Ireland peace process - to turn from hopeless and seemingly inevitable conflict to peace and partnership. The temptation is to dismiss this as Downing Street "spin". Yet witness again the president's eloquence in citing the Irish experience as proof that old patterns of division and hatred can be broken when one generation decides to do so.
Witness, too, his promise to emulate Mr Blair in his devotion of time to see the promised road map through to an actual Israeli/Palestinian settlement.