The Potomac Room of the Fairfax Hotel boasts all the accouterments of an upper- crust saloon: lots of wood and leather, high- priced highballs, prosperous-looking patrons and John Eaton. He's the fellow at the baby grand.

"Now I'll try a little number -- perhaps you've heard of it -- called 'Have You Met Miss Jones?' " Eaton said the other night in the midst of his first set. More than filling out a three-piece pinstripe, he was seated at a Steinway whose lid had been removed.

"Are you going to sing it, too, John?" wondered a lady in black nearby.

"No, indeed. No, indeed." He mopped his brow under shaggy brown bangs. He sniffed: he had a cold.

"It's very easy," she pressed.

"That's what you say," the pianist shot back, and, squinting down through wire- rims, plunged into the Rodgers and Hart tune free of the lyrics.

The lady, settling back in a crimson chair, chuckled and tapped a high heel. A bank of men in blazers and women in designer dresses swayed ever so slightly to the beat. Farther out from the keyboard, against a wall panneled in burnished English pine and festooned with etchings of fox and hound, a chap in an ascot chatted with a younger woman flashing a fixed smile. He looked and talked like the late Shah of Iran; she looked and listened.

In a nook to the side, a few stout gents with sleeves rolled up paid no attention to the hotel's request, printed on a card, to "lower your conversation while (John) is playing."

"Merrill Lynch. . ."

"Strategic planning. . ."

"Upgrade to first class. . ." they blurted between guzzles from shot- glasses and clinks of ice. The lady in black, tapping, shot them an icy stare; Eaton seemed unperturbed.

"I usually ignore people who are being obstreperous," he said later. "Particularly in this room, I'm so intent on my playing that I don't tune in. Over the years, though, in different lounges, I've gotten quite an earful. Some people believe that pianists are just part of the furniture, and they speak as if you weren't there. I find it very amusing. You hear fragments of things: spats between a man and a woman, a family quarrel, a business discussion. The Merrill Lynch crowd: They're completely oblivious that there's music in the room."

He finished the Rodgers and Hart number with a jazzy little flourish. There was applause, which he acknowledged with a bow from the neck.

Eaton has played in bars about town for nearly a quarter-century, and is the dean of the profession hereabouts. With improvised renditions of jazz standards and show tunes, ballads, love songs -- maybe a riff from Bach to keep the customers on their toes -- his music is more than to drink by. (A good thing, too, what with cocktails running to $3.50 a throw, and nothing but peanuts to nibble.) It's often interesting, cleverly spliced, and always done with assurance and clarity.

He 's been at the Fairfax for the last three years. The Potomac Room might not pass for a proper piano bar, where you can sit by the keyboard and sing along, but Eaton said he rather likes its distanced formality. Though he hides what he's up to with banter, he generally gives a full-blown recital.

"At the Snuggery, John, you had all that vocal help, remember?" the lady in black said. Eaton laughed. "That's all I needed."

He launched into "A Nightingale Sang in Berkeley Square." "Anybody know who wrote that? Was it Roger Tory Peterson? Kay Summersby?" (Actually it was the team of Sherwin and Maschwitz.) He continued with a medley of Cole Porter tunes, some Gershwin standards, a Joplin rag -- paused to nod approvingly at a guest in white dinner jacket -- tackled Jerome Kern and more.

The lady in black stuck around past midnight. "I've been following him around for so long," she said, and a worried look crossed her matronly face. "Do you think I could be classified as a groupie?" JOHN EATON -- In the Potomac Room of the Fairfax Hotel, 2100 Massachusetts Ave. NW, from 9 to 1 Tuesdays through Saturdays. 293-2100.