Clearly, the final point had been scored by Sir John himself. The Council had triumphed in resolving the deadlock and, by rushing to the press, he made sure the first blush of credit was his. We know this mattered because on his return to the chamber, he was personally ticked off by Madeleine Albright of the United States. Breaking the news was the job of the council presidency, held by Italy, she protested. The Secretary of State-designate, in other words, wanted to get to the cameras first.
Sounds a little childish? Well, indeed. Like any board game, this had a dimension that was strictly kindergarten. France's brief show of blocking Annan's appointment last week was essentially revenge against the Americans for casting their veto against a second term for Boutros Boutros-Ghali last month (the Egyptian is a fluent French-speaker, which the Ghanaian Annan is not, and a second Boutros-Ghali term had been France's preference). British diplomats, by contrast, were convinced for weeks that France was "heading into a brick wall", and could barely contain their glee.
For weeks UN headquarters had been drowning in torrents of mostly pointless speculation, rumour and intrigue. Correspondents were at one turn probing officials from their own national missions for clues of the game's progress and at the next turn fending off the questions of officials from other missions. But this was also a serious game, with high stakes - hence the intensity of the play. To the casual observer, the question of who should lead the UN might seem boring. For the protagonists, though, it mattered very much, and especially to Britain and France.
Because London and Paris - by virtue of an arguably outdated quirk of post-Second World War history - still have their seats among the Big Five permanent members of the Security Council, along with the US, China and Russia, they care deeply about the UN. It is the institution that still gives them reason to believe they are top players on the world stage, however much others call that an illusion. British foreign policy gets done in three places - Whitehall, Brussels and New York. For the French it is the Quai d'Orsay, Brussels and New York.
If for no other reason than diplomats' love of intrigue, Britain was never going to keep out of the succession debate. But London has also been quietly fretting in recent months about the dwindling stature of the UN, its penury and its low standing in the US. The Government wanted to be sure, therefore, that the UN's next Secretary General was a figure capable of lifting the gloom and giving the institution new energy and respect.
France, meanwhile, has been outraged by Washington's ham-fisted display of power since June, when the US leaked its decision to the New York Times to exercise its veto, come what may, against Mr Boutros-Ghali. "It really touched a raw nerve," one French official noted. "America presented us with a fait accompli, and we could not just accept that."
Britain's strategy was different. Ministers, including John Major, concluded weeks ago that if the UN was going to uphold the unspoken convention in favour of Africa holding the post of Secretary General for another five years, Mr Annan was the best man available. The British government was not necessarily opposed to a second Boutros-Ghali term, but it understood before anyone that the US was not going to retract its veto of him. The challenge was how to work with the US to build support for Mr Annan, and undercut the French. It had to work furtively, however - to have confirmed widespread suspicions that the Ghanaian was the "Anglo-American choice" could have been fatal to his candidacy.
"It was our view that the best approach was to allow the innate weight of Annan's case and his qualifications to bear down on everyone gradually," one senior Briton said on Friday night. "Once everyone looked seriously at Annan he was always going to measure up to expectations." To help push the pace a bit last week, British diplomats began a campaign of corridor murmurs. The French "cocked up", it was put about; African delegates were warned that unless there was quick consensus on Annan, the Security Council would move on to look at candidates outside Africa.
There is probably much more we do not yet know - of trial balloons popped before they ever took flight and of dastardly schemes buried as quickly as they were conceived. For now, though, score up a big win for Britain and the United States and an embarrassing defeat for France. Africa is the winner too. Oh yes, and Mr Annan.