Tommy Flanagan played brilliantly behind Ella Fitzgerald, and on a few memorable occasions, Bill Evans beautifully supported Tony Bennett (and vice versa). But great pianists don’t always make great accompanists. The stylistic excesses that make them special — Oscar Peterson’s breakneck speed, for example, or McCoy Tyner’s chordal thunder — can work at cross purposes with a vocalist who is trying to create a mood or tell a story.

But when you’re a great pianist accompanying yourself, an art at which Andy Bey has excelled during his late-in-life reign as sui generis ballads king (hear his superb new album, “The World According to Andy Bey”), the rules change. “Nobody can play for me like me,” said the Newark, N.J., native — not with hubris, but the understanding that a singer with his bottomless range and ebbing and flowing power demands a pianist who is with him note for note — or not.

“I’m not about playing all over the piano,” said Bey, who performs Dec. 7 at the Kennedy Center as part of a “Jazz Piano Christmas.” “I play when I want to play. Sometimes, I have piano and no voice, and sometimes voice and no piano. I might play anything against the vocal line. I like starting songs on a different tonic than usual to make things interesting harmonically, and music in which chords go off. I’m not afraid of dissonance. I’ve been working on that for 40 or 50 years. I keep evolving.”

“I like where I’m at now. I’m 74, but my voice is still developing. And as a writer, I’m trying new things that are driven more toward what I’m thinking now. Still, I love the American song. Some songs are so beautiful. Melody frees you. If you know the melody of a song, you can go anywhere you want to.”

Andy Bey (Courtesy of the Kennedy Center)