When Fred Astaire first sang Irving Berlin’s “Puttin’ On The Ritz” in 1930, the lyrics were not about the upper class blowing off steam. Rather, they depicted African-American domestics celebrating on their night off. Only for subsequent generations was the lyric changed from an instruction to go “where Harlem sits” to “where fashion sits.” So it’s fitting that the new revue, “Singing Astaire,” being performed at Birdland, is a jazzy tribute to one of the greatest figures in the American musical experience.

Astaire’s trademarks were a top hat and a formal tailcoat, but he always claimed to prefer a more casual style. The three co-stars – Christopher Gines, Hilary Kole, and Eric Comstock – acknowledge this appropriately; the only tie in sight is around Mr. Gines’s waist, Astaire-style. There’s an emphasis on the three singers as a vocal group, with very modish, sophisticated arrangements by Ms. Kole.

Five years ago, these same three performers first mounted “Our Sinatra,” a cabaret-style tribute to the Chairman of the Board. For the new production, they’ve added a drummer, David Silliman. The musical inspiration comes as much from Mel Torme’s cool-jazz makeovers of these tunes as much as the Broadway and Hollywood originals.

The three are at their best when stitching tunes into elaborate medleys. The opening combines bits and pieces, verses and refrains from “Steppin’ Out With My Baby,” “Top Hat, White Tie, and Tails,” and “Puttin’ on the Ritz” (which they rhyme with “Frederick Austerlitz,” Astaire’s given name). They also incorporate the bass note vamp from “Sidewinder,” Cuban montuno patterns, substitute harmonies, and, in a few cases, substitute melodies.

Of the three, Mr. Gines has the prettiest voice, Ms. Kole is the strongest on up-tempo swingers and Mr. Comstock is the best balladeer. Ms. Kole shines on a lightly Latin “Night and Day.” On “Isn’t This a Lovely Day,” the sultry Ms. Kole quickly heats the raindrops into steam. But the highlight of the whole production, surprisingly, is its quietest and most intimate moment: Mr. Comstock makes Johnny Mercer’s normally boisterous “Something’s Gotta Give” sound as reflective and introspective as anything by Cole Porter. The singer’s reference to himself as “an old, immovable object” suddenly sound self-deprecating as he contemplates the vast, mysterious sky.