A GOOD JAZZ pianist is like a martini. An excellent one relieves you of any need for the martini. Tommy Flanagan, most critics agree, was not merely excellent but one of the best. When he died this month, at 71, he joined a parade of jazz-world losses that had seemed to accelerate as the 20th Century closed.

As the 21st opened, only a few golden-age figures were still performing; among them was Flanagan, who appeared at the San Francisco Jazz Festival in October. His death, on Nov. 16, was brought on by complications from a brain aneurysm suffered a decade before.

Many New Englanders know Flanagan through his trademark rendition of "Peace," which has long opened public radio station WGBH's weeknight jazz program. Despite years of repetition, it remains mystifyingly fresh.

Flanagan's art is what many people today associate with a certain type of bar or reception, a pleasant tinkling in the background during drinks. But jazz piano is far more complex than that, with a history rich in achievements.

It emerged from late 19th Century ragtime, and found its modern footing in Harlem, in the 1920s. There, it was shaped into the loose-jointed form known as stride piano by the likes of Eubie Blake, Fats Waller and Art Tatum.

As a child growing up in Detroit, Tommy Flanagan heard these players on recordings. He was so excited by their sound that at age 11, he chucked the clarinet, and took up the piano.

For a boy interested in jazz, Detroit in the 1940s and '50s was a fine place to be. The music flourished in clubs there, and leading players visited regularly. Flanagan was drawn to the emerging sounds of bebop, and was able to hear Charlie Parker and Dizzy Gillespie in live performances.

In 1956, Flanagan moved to New York, and proceeded to blend in. He became known as a top accompanist and exquisite sideman, turning up on major recordings by John Coltrane and Sonny Rollins, among others. For about 20 years, he played alongside Ella Fitzgerald, who credited him with coaxing the sound she heard in her head out into the world.

Flanagan seldom placed his own playing in the spotlight. And it became a source of increasing frustration to careful listeners, who knew that something special was going on wherever Flanagan sat in.

The turning point seemed to come in 1978, when Flanagan suffered a heart attack. He stopped accompanying Fitzgerald and gradually moved into trio work. The classic ensemble of piano, bass and drum seemed made for him, and when Flanagan was in his 60s, he released a series of albums that drew wide acclaim.

Jazz Poet (a phrase conferred on Flanagan by New Yorker writer Whitney Balliett) came out in 1989. In 1990, Billboard selected it as one of the best albums of the year. Flanagan topped readers' polls for Down Beat and Jazz Times magazines. Grammy nominations rolled in. A new generation of fans was discovering jazz, and Flanagan was a favorite.

His popularity hinged on a fluid, rhythmic style that had much in common with the vocalizations of Fitzgerald. Both possessed a lyrical grace. But above all, they shared an unrivaled clarity of sound.

In Flanagan's case, the clarity emerged partly from pianists' collective response to bebop. It was not possible to incorporate the florid style of an Art Tatum into bop; a much more streamlined approach was needed. In Flanagan's hands, the streamlining turned over the years into an almost transcendent elegance. He did not seem to play the piano so much as call upon it.

A few years ago, I had the chance to see Flanagan perform in the Boston area. He appeared aged and almost frail, which made his keyboard dexterity seem all the more remarkable. The bassist that night was Peter Washington, a frequent and much younger collaborator. I do not recall the drummer.

The three were well into the set, between numbers, when Flanagan paused. For several seconds, he stared at the keyboard as though he could not make up his mind about something. The audience tittered politely.

The silence expanded as Flanagan continued to stare. He shook his head. Some in the audience no doubt knew of his heart problems, and may have feared, as I did, that they were witnessing a stroke. No one dared to move.

I found myself fixing on the bass player. He was neat as a pin in a jacket, starched shirt and tie. His face betrayed neither nervousness nor embarrassment. Instead, it wore an unchanging expression of patient dignity.

A full minute passed. People shifted in their seats.

The bassist did not look at Flanagan, or laugh; he permitted himself a trace of a smile. The room was filled with a sense of barely suppressed panic, but the bass player remained serene.

I realized what I was seeing in his face was profound respect, and the deepest faith in another human being I was ever likely to witness. They were ideals made flesh, in much the way music expresses things we cannot ever prove.

At last Tommy Flanagan put his hands on the keys. He played, just as though nothing had happened, as though a melodic line might be mislaid as easily as a pair of glasses. Washington pressed his fingers on the strings, and bent into the chords. His face did not change at all.

M.J. Andersen is a Journal editorial writer and columnist.