What is more, we have been round this course before. Seven years ago Javier Perez de Cuellar went to Iraq in a last-ditch attempt to persuade Saddam to leave Kuwait before he was driven from it. He was left to cool his heels for 24 hours in the ante-rooms of one of those now infamous "presidential palaces" before being received. The rest needs no recounting. Can this secretary general do better? Maybe not. But if he fails, it will not be because of bad manners.
The first epithet that comes to mind with Kofi Annan is "dignified". There is an unruffled quality to him and everything he does, the gracious wisdom of the African gentleman of a certain age. Even when critical he is the epitome of politeness. Never does he lose his cool. A slight shifting of weight from one foot to the other, perhaps, in a moment of high strain, an aide reports, "that's about all the tension you can see".
So how will he cope with President Hussein? "His instinct always is to avoid confrontation and seek consensus," says another colleague. But these are qualities that will not avail him much in Baghdad as he presents Britain and America's demands. A little tinkering around the edges perhaps, to save the dictator's face; but on the substance he has no choice but to be firm. The first hint of fudge or waffle, the first whiff of curbs on the powers of the weapons inspectors - and cruise missiles and F-117 Stealth fighters will be about their destructive business. But never mistake Mr Annan's gentleness for evasiveness or fear.
It was 13 months ago that he replaced Boutros Boutros-Ghali, the Egyptian Copt whose Gallic conceits and patrician ways the Americans could no longer stomach, to become the seventh Secretary General of the UN, and master of the hideous skyscraper standing sentry over 41st Street and East River in midtown Manhattan.
The official reason Washington defenestrated Mr Boutros-Ghali was his failure to streamline the UN's bureaucracy. Yet the man the Clinton administration turned to was a "bureaucrat" par excellence. Unlike his predecessors, Mr Annan rose through the ranks to the job. He has spent more than 30 years working for the UN - his entire career barring a spell at the Massachusetts Institute for Technology where he took a masters degree in management in the mid-1970s. But thus far he has delivered his end of the bargain, chopping 1,000 jobs within the secretariat, and reducing the organisation's budget.
Kofi Annan is a diplomat's diplomat. He gives no hostages to fortune, and can reveal the lightest of touches. "I now speak English with a French accent," he smiled, when asked in 1996 about French hostility to his candidacy. In truth, as everybody knew, he spoke very decent French, and Paris's quarrel was not with him but with the steamrollering tactics of a superpower. Anyway, the line helped win over even Boutros-Ghali loyalists, who knew their man was doomed.
Most important now, he gets things done. "Kofi's a manager. He knows his brief, he can grasp an issue quickly and doesn't just spout a line," says a European diplomat who knows him well. "Equally important, he recognises his limitations and picks clever people to work under him, and he organises better. Boutros used to isolate himself on the 38th floor. Now the co- ordination, the whole flow of the place is far better."
The clever people he has chosen include Mary Robinson, the former president of Ireland, to be the UN's human rights representative, and Gro Brundtland, previously Norway's prime minister and a qualified doctor, to head the World Health Organisation. In recognition of the huge demands on himself imposed by travel and protocol duties, he appointed Louise Frechette, a Canadian, to be Deputy Secretary General. Mr Boutros-Ghali, the proud and prickly autocrat, ruled alone.
But the going will get far harder when Mr Annan embarks on reforms that threaten direct national interests - not least those of the Third World of whom this secretary general would seem to be a natural champion. Take his insistence that human rights should be a constant criterion in UN decision-making. The Group of 77 developing countries is most uneasy - as demonstrated by his involvement in the Zaire crisis last year. Mr Annan went to the Organisation of African Unity summit in June and secured agreement on a mission to examine alleged abuses by Laurent Kabila's regime in the renamed Congo. But next to nothing has come of this mission.
Part of the explanation lies in Mr Annan himself. He is from Africa, yet not of it. He is not a product of Africa's colonial struggle, but the scion of a family of traditional chiefs of the Fante tribe. He left for America on a Ford Foundation scholarship in 1959, just after the former Gold Coast won independence from Britain. Three and a half decades later, by then Under Secretary General in charge of UN peacekeeping operations, Kofi Annan complained of the problems in attracting African contingents, "probably because their governments need their armies to intimidate their own populations". Like half of all Ghanaians, at home or abroad, he seems to be a Manchester United fan. His Swedish second wife, Nane Lagergren, is a lawyer and painter, and a niece of Raoul Wallenberg, the legendary diplomat who saved Jews from the Holocaust only to be murdered in Stalin's jails.
Given that westernised background, and the perceived patronage of the US, "it's no wonder some people are suspicious of him," a close UN-watcher points out. "It's vital he's not seen as being a sort of diplomatic Uncle Tom, in Washington's pocket. He couldn't survive as Secretary General if he was." Nor is he one. But Mr Annan will require every drop of diplomatic skill to deal with the US, the UN's harshest critic and most egregious financial miscreant, yet the one country from which the organisation cannot be estranged if it is to retain any credibility.
Under Boutros Boutros-Ghali relations were appalling; ultra-patriotic militias in darkest Montana even believed black-uniformed men from the UN were coming to take them away. The Republican Congress so detested him that the party's 1996 presidential contender Bob Dole gave the wretched "Boo Boo" a demon status to rival that of Saddam Hussein himself. But Mr Annan has never minced his words, whether over the US failure to cough up the $1.4bn it owes the UN or its queasiness about risking American lives under international command. "The impression has been created that the easiest way to disrupt a peacekeeping operation is to kill Americans," he tartly observed after the debacle of Somalia in 1993 when 18 Americans died. And whenever he goes to Washington, he reminds his hosts (with exquisite politesse, of course) about the small matter of that unpaid bill.
Through thick and thin, however, Mr Annan's reputation survived - even as that of peacekeeping foundered. The tribulations and humiliations of the UN in Bosnia sounded the knell of a brief "golden age" of the United Nations, the years around 1990 when Cold War foes became friends, the dream of a "new world order" flourished, and the UN could assemble the mightiest coalition in history to drive President Hussein from Kuwait. Now the UN is so broke it can barely finance the peacekeeping operations that remain and, in the wake of Somalia and Bosnia, the entire function is being reassessed.
"The good man from Africa" was the headline on one fulsome profile when Mr Annan became the first Secretary General from sub-Saharan Africa; Kofi Annan "could make the world a better place". Such warm feelings were universal, a measure of the respect and popularity Mr Annan enjoyed. The esteem is little short of miraculous given his career in the UN system, a hyper-sensitive and politically charged bureaucracy, elephantine in size, elephantine in pace, and elephantine in its memory of the merest slight, real or imagined. Somehow, though, Kofi Annan made no enemies.
But to make the world a better place? That is a burden of expectation which few should be asked to shoulder. The UN may be primus inter pares among international institutions but its Secretary General is not God. He is the more or less humble servant of the "Big Five" permanent members of the Security Council. "Speak softly, and carry a big stick," was Teddy Roosevelt's advice for future statesmen. With his quiet, purring baritone, Mr Annan more than qualifies on the first score. But, like his predecessors, he has no stick - or, to be precise, only the feeble wand the"P-5" is ready to give him.
Progress at the UN usually obeys the principle of the lowest common denominator. If Kofi Annan changes the world, it will be thanks to either moral suasion or a transformation of the institution he leads. And, indeed, change is afoot. Pressure is growing for the first changes in the make-up of the Security Council since 1945. There are demands for a standing UN rapid- reaction force, and in a year or so we may have a permanent international court, under UN auspices, to track down and punish war criminals and human rights violators. One of its first defendants might be Saddam Hussein. But that is for tomorrow. Let us merely hope that this weekend in Baghdad, the good guy prevails.