The American president and the Soviet chieftain were signing the historic nuclear treaty, and at that very moment, in a posh restaurant halfway between the White House and city hall, the mayor of the capital of the Western world's most powerful nation and the ombudsman of the world's most powerful local newspaper were eating each other's lunch.

The mayor had phoned the ombudsman with a complaint, just like any other reader, except it wasn't about a story that appeared in The Post, but a letter the ombudsman had written.

"That wasn't a very nice letter to write to one of my constituents," the mayor had said on the phone. "Let me read it to you. 'Dear Mr. Z.: I received your three-page letter outlining the many achievements of Mayor Barry and asking for my comments. I have referred the letter to one of the editors of Metro because I know very little about what goes on in the District and neither, I suspect, does Mayor Barry.' "

Hizzoner read the blasphemous letter -- which I couldn't recall writing, though it did sound like me -- in an almost childlike monotone, without a trace of enmity. It wasn't my first awkward mayoral confrontation, but the other had occurred some years back and I was only a witness. The chairman of a civic celebration in New York City had made the blunder of inviting the New York mayor to the same speakers' platform to which a crusading rabbi who had been after the mayor's hide for months was invited. "You've heard of Rabbi Wise?" the chairman asked the mayor. "Of course," he snarled. "He's abused me often enough." Retorted the rabbi: "I've abused you often, Mr. Mayor, but not enough."

That was nothing compared with the contretemps I now faced. The ombudsman writes many letters, I explained, and these missives to unhappy readers become shorter and shorter as time goes by. And to keep them interesting, sometimes one is tempted to turn a cute phrase, and without a secretary, these things just get out.

"No secretary?" Mayor Barry said. "I can't believe it." He invited me to lunch.

Mayor Barry ordered pressed veal; I, angler fish and lobster. I was determined not to bring up any unpleasant matters, certainly not the recent weekend in the Bahamas, nor why the District needed a boxing commissioner.

It was "Joe" from the start, as you'd expect from a big-city mayor. He said that it was a shame I had no secretary and that he'd spoken to Publisher Don Graham and Executive Editor Ben Bradlee about it.

He refilled my coffee cup, and this gracious gesture turned my mind back to the previous time I'd broken bread with a mayor, at a dinner with Ed Koch at Gracie Mansion. Still fresh in my mind was the vision of the liveried maids and butlers serving the mayor first, his guests last.

"Dinner at Gracie Mansion? New York gives him a mansion and I don't even get a housing allowance. Even the D.C. school superintendent gets $10,000 a year for housing. How come The Post never points this out?"

I promised I'd mention this to The Post's editorial page editor. "One other thing," he said. "Why did The Post put that story about the Bahamas on page 1, up there with all those stories about the president and Mikhail Gorbachev?" I said I'd ask Managing Editor Len Downie about that.

So engrossing was our conversation that I was halfway through the meal before realizing the waitress had given each of us the other's lunch. The mayor had already finished my fish. "How was your veal?" I asked mischievously. "Tasted funny," he said. "I don't care much about food. I just eat to stay alive."

Over his protests, I shared what was left of the veal. The waitress panicked but the mayor soothed her, saying he didn't know one dish from another.

The check arrived. This was the moment of truth. I was determined to pick up the tab and to do it without seeming rude because, after all, it was the mayor who had invited me to lunch. We both pulled out our American Express cards. The maitre d' rushed over. "With a mix-up like that, I cannot let either of you pay," he said.

Breaking bread with the mayor had been a charming experience. If the mayor ever invites you to lunch, I'd recommend you accept without hesitation.