"Iraq No, Morocco Yes. Why?" a billboard asked above James Baker's head. Was he not the US Secretary of State who ordered Iraq to end its occupation of Kuwait seven years ago? And would not the same James Baker, now special envoy to the UN Secretary-General, now have come to order Morocco to end its 22-year occupation of the western Sahara?
So it was that the supplicant refugees - the 140,000 Saharawis in Algeria whose Polisario guerrillas had harried the Moroccan army for 16 years until their 1991 ceasefire - stood in the desert sandstorm outside Tindouf as Mr Baker, slayer of the Iraqi army and nemesis of Saddam Hussein, arrived in majesty.
He emerged from his jeep sporting a peaked UN cap; perhaps aware that this made him look like an incongruous baseball star, he took it off within seconds.
And there, bronzed beneath the sun, stood the man who would decide their fate, he who faced down the Beast of Baghdad, a sudden flourish of his left hand freeing half a dozen white doves which fluttered above us to cries of approval from the sand-blasted masses. Many are the ageing British proconsuls - sent to the far corners of Asia to adjudicate on tribal frontiers - who would have understood the gesture.
We didn't see these doves back in 1991, of course, but this was the new model James Baker, peacemaker extraordinaire. He came ready to listen - or so he repeatedly told the exiled and Ruritanian "government" of the western Sahara - to the Saharawis and Moroccans, the Algerians and, no doubt, to the United States of America.
What the Polisario want is their own independent state in the western Sahara, along with its phosphates and rich fishing grounds. But King Hassan of Morocco, Commander of the Faithful, is still offering the Saharawis only limited autonomy.
Algeria, the Polisario's traditional supporter, does not want to give King Hassan any territorial victories, but it is now distracted by a savage internal war.
Much more to the point, King Hassan remains one of Washington's faithful allies in the Middle East. He is one of the few Arab leaders who is still on speaking terms with the Israelis now that the "peace process" - initiated way back in 1991 by a man called James Baker - is dead.
Is Mr Baker, therefore, going to support the demands of the destitute and sick refugees - people whose east European support dried up with the collapse of the Iron Curtain - against America's royal friend in Rabat?
Pathetically, the Saharawis in their blue and black robes, shrieking their welcome from the sides of the track through the desert, their ramshackle army wiping the sand from beneath their tin helmets, believed that the steel-hearted Mr Baker might be swayed by their obvious emotions.
"Surely when he sees our people like this, he will understand our suffering and our need for independence," a Polisario factotum, cowled in a black shawl, vouchsafed to us. As he spoke, a flurry of American military personnel - blue-bereted, but with very large US shoulder flashes - pushed their way through the crowd. "Mr Baker is a powerful man - and we need a powerful man to help us," he said. Nearby another billboard proclaimed: "Mr Baker - remember Big Fish versus Small Fish."
But powerful men understand weakness as well as strength, and it was the Big Fish of Morocco who opened the Maghreb to Israel (even if it is now planning to close the Rabat-based secretariat in charge of Middle East economic summits). And it was Algeria which organised the final return of America's embassy hostages in Tehran a long decade ago.
Despite the presence of a well-maintained Russian BMP armoured vehicle - crewed by Polisario men - close to James Baker's jeep, Algeria has no desire for a continuation of the war.
It must have come as a relief for Mr Baker when he entered the straw- roofed chamber of a stone desert house to meet the sheikhs of the Polisario's four refugee camps in south-west Algeria, the nearest the Saharawi people have come to democracy in exile.
Tired and unsmiling, he later emerged from talks with the Polisario's "president", Mohamed Abdul-Aziz, to say all the right things: that he was impressed by his welcome, that it was a tough problem but not a hopeless one - "or else I wouldn't be here" - and that this was merely a fact- finding trip.
He welcomed the "very, very generous humanitarian gesture of support for my mission" - the release of just 85 out of 2,000 Moroccan prisoners, some of whom have been held for 21 years in the desert, by the aforesaid "president".
Then he went on to add that if the UN's own peace plan - which includes a referendum of Saharawis in Algeria and in Moroccan-ruled western Sahara, prisoner exchanges, and a reduction of troops - could not work, then he would have to advise the UN Secretary-General on "what other steps could be taken".
And there's the rub. For what is likely to have interested Mr Baker is the degree of war-weariness of a people who left their homes 22 years ago for the most arid desert in the world. Left their homes to live in heat and dust, drinking the filthiest water the UN has ever come across in its history of refugee assistance, their teeth and bones brittle from lack of vitamins and too much nitrogen in the water. War-weariness is a vital element of refugee morale.
After all, were the Palestinians not weak and war-weary when Mr Baker invited them to make peace with Israel in 1991?