The trombonist Wycliffe Gordon is one of the most visible young musicians in the city. Hardly a week goes by when his outgoing personality isn’t livening up the bandstand somewhere. Yet the opportunities to hear him leading his own group in a major club are surprisingly few and far between.

This week at Dizzy’s Club Coca-Cola, Mr. Gordon is appearing with a quartet – a rare setting for a trombonist – and he is making the most of the opportunity. He is backed by two fellow veterans of the Jazz at Lincoln Center Orchestra, bassist Reginald Veal and drummer Herlin Riley, along with Gary Gillespie, a young pianist not previously known to me.

During Wednesday evening’s late set, Mr. Gordon’s quartet essayed a program of jazz standards plus one historically minded original. The concert was notable for its casual success in covering tunes and styles from roughly 40 years of jazz history.

To begin the set, Mr. Gordon reached even further back in time by playing a series of grunts on the didgeridoo. When that Australian instrument yielded to the more familiar trombone, a buzzy melody took the shape of Duke Ellington and Juan Tizol’s “Caravan.” On the first chorus, however, Mr. Gordon utilized a tight, humming tone that sounded like Mel Blanc blowing into a rubber band. Then he switched to improvisation mode, and the piece was updated from Ellington to something more like the Jazz Messengers playing “Night in Tunisia” – this “caravan” could easily have been traveling through Tunisia.

Mr. Gordon followed this with a bright and Armstrongian “On the Sunny Side of the Street,” complete with his own satchel-mouthed vocals. In a move suggestive of New Orleans, every time the melody would reach the middle of the bridge (the line “blues on parade,” the other three guys in the quartet would let out a long, dull moan. This was the first chance to hear what Mr. Gillespie was capable of, and he ably mixed blues phrases with gospel sighs and tinkling reminiscent of Count Basie.

This was followed by the sole original, Mr. Riley’s “Morosa Mirage.” A 1960s-style modal piece, this tune almost could have been a bonus track from Herbie Hancock’s “Maiden Voyage.”

“Just Squeeze Me,” another Elling ton standard, gave Mr. Gordon a chance to hold a conversation with himself, with the two participants being a low, moaning sound and a smooth, more romantic approach. When a cell phone rang in the audience, Mr. Gordon waited for a break in his phrase and then piped up, “Hello” – now extending the conversation to a third voice.

Dizzy Gillespie’s “Blue ‘n’ Boogie” allowed the quartet to kill several birds with one stone: The tune is an authentic blues from the dawn of the bebop era. A guest pianist, Dan Nimmer of the Lincoln Center Jazz Orchestra, sat in, but Mr. Gordon’s biggest surprise was a scat solo that incorporated a number of early bop anthems like “Salt Peanuts” and “Poppity Pop.”

He concluded, surprisingly, with Mr. Riley singing the rather goofy-but-authentic lyrics to the traditional New Orleans parade march “Bourbon Street Parade.” It was like he was ending jazz where it began.

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The last time I heard the Broadway veteran Betty Buckley perform at Feinstein’s, her band leaned toward a Celtic-tinged new age sound. Though she is reprising much of the same music this week at the Blue Note, she’s given it a stronger beat that makes it sound like it belongs in a jazz club. Ms. Buckley isn’t trying to fool anyone into thinking she’s Ella Fitzgerald, but by varying her material and allowing it to shape her voice, she has come up with a copacetic blend of genres.

Ms. Buckley’s Blue Note run is directed, as always, by the excellent pianist Kenny Werner, whose arrangement of Stephen Sondheim’s “Anyone Can Whistle” was a highlight of Wednesday night’s early set. Here Mr. Werner has the melody answered by a series of phrases by the clarinet (Billy Drewes) and the violin (Todd Reynolds) but voiced in discordant unison. Mr. Sondheim’s music, fortunately, is equal to the challenge, but Mr. Werner’s over decorated chart of the blues-driven hit “Cry Me a River” was less successful. This included, among other things, a funk vamp reminiscent of Miles Davis’s “In a Silent Way,” and it was almost too much musical weight for that bone-simple tune to bear.

Ms. Buckley, however, can also put over simple and poignant numbers. She made “Stardust” seem celestial, and delivered a pair of Rodgers and Hart standards like folk songs. By contrast, she turned Brenda Russell’s “Get Here” into jazz – or something very much like it.

Gordon until June 4 (Broadway at 60th Street, fifth floor, 212 258-9595). Buckley until June 4 (131 W. 3rd Street at Sixth Avenue, 212-475-8592).