There’s a great recording by Sarah Vaughan from 50 years ago, “Swingin’ Easy,” on which she introduces her drummer as “Little Roy Haynes.” It seems to me that short dudes are particularly well constructed to play the drums: So many of the greatest in jazz, among them Chick Webb, Buddy Rich, Art Blakey, and, yes, Roy Haynes, have been dynamic, diminutive dynamos.(An exception that might prove the rule was Sid Catlett, who so stood out from his fellow percussionists that he was given the nickname “Big.”)

In his opening set at Iridium on Wednesday night, the spry and sharp dressed Mr. Haynes was no less energetic than he was five decades ago. He made his presence felt on every note without any of the grandstanding and needless soloing drummers sometimes throw in to attract attention. Instead, he simply kept his quartet on track, a locomotive at once pulling and pushing his train to a clear destination.

As Mr. Haynes recounted during a discussion at the Jazz Museum in Harlem last week, he first arrived in New York in 1944 to work with Luis Russell’s orchestra, and also toured with Louis Armstrong’s big band. He is best known as the drummer with the classic Charlie Parker quartet (which co-starred the equally young Miles Davis), and spent many years on the road with Sarah Vaughan. He has also led his own groups since the 1950s, proving himself the third of the great modernist drummer-bandleaders, after Blakey and Max Roach.

Mr. Haynes’s most recent CD, recorded at Birdland in 2002 and released last year, is titled “Fountain of Youth” (Dreyfus 36663). The drummer turned 80 in March, but the rest of his current quartet is composed of youngsters: alto saxophonist Jaleel Shaw (previously known for his work in the Mingus Big Band), pianist Martin Bejerano, and bassist John Sullivan. The three sidemen’s combined ages may equal that of their leader – barely – but their collective energy and drive cannot surpass that of the inestimable Mr. Haynes.

A hallmark of Mr. Haynes’s live performances is that his ensembles often cram a lot of music into relatively short songs; in this very full 80-minute set, the quartet found time for seven numbers. Two standards, “My Shining Hour” and “We’ll Be Together Again,” primarily featured Mr. Shaw, who like nearly all contemporary saxophonists spent much time learning from John Coltrane. In his adaptation of Coltrane’s sound to the alto sax, he reminded me of Mr. Haynes’s frequent sideman, Kenny Garrett. On “We’ll Be Together Again,” he achieved a powerful tone mostly in the lower register, but when Mr. Haynes called Dave Brubeck’s “In Your Own Sweet Way,” Mr. Shaw evoked Paul Desmond, playing this tune mostly in the upper register.

The band’s tour de force was the exuberant staccato melody of Thelonious Monk’s 1966 “Green Chimneys,” which can also be heard on “Fountain of Youth.” Here’s a showpiece for a percussion-driven quartet that never lets up: The rhythm, especially as essayed by Mr. Haynes, is more essential to the tune than the notes, and the song opens with the drummer stating the melody. In the sidemen’s solos, Mr. Shaw accentuated the jerks and jagged edges of the tune. Mr. Bejerano, in contrast, took it upon himself to smooth out the melody line. The rest of the group then took a well-earned rest while Mr. Bejerano played a brief, unaccompanied feature on “Lover Man.”

The quartet wound up with “Inner Trust,” composed by a longtime associate of Mr. Haynes’s, pianist Dave Kikoski. This is obviously a piece the drummer is partial to, since he featured it on his 1998 album “Praise” as well as “Fountain of Youth”; on this night, it provided a vehicle for Mr. Shaw’s soprano saxophone playing. In a surprise, this almost classical tune – the most lyrical number of the evening – occasioned a standout drum solo from the leader, giving our ears as much of a workout as the skins.

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For years, cabaret singer Paula West was known for her slow, sensual phrasing – she has as many degrees of “slow” as the Inuit have words for “snow.” But for the last few years, Ms. West has been concentrating on uptempo numbers. To everyone’s surprise, she is becoming one of the most hard swinging vocalists on the current scene, particularly by the standards the Oak Room of the Algonquin, where she just opened her annual one-month run.

In her show Tuesday night, Ms. West stressed rhythm and imagination. The latter came through particularly in her choice of repertoire. Working with longtime musical director Eric Reed on piano (and bassist Gerald Cannon and drummer Willie Jones III), she performed some traditional show tunes written for black performers (“Too Darn Hot,” “Happiness Is Just a Thing Called Joe,” “Taking a Chance on Love”), but the majority of her songs came from outside the Broadway-Great American Songbook tradition.

Ms. West sang Nina Simone’s “See Line Woman,” accompanied by just bass and drums, and rendered Bob Dylan’s “Mr. Tambourine Man,” so that listeners could actually discern the words and narrative (such as it is) in all their surreal glory; the showstopper was “Folsom Prison Blues,” re-harmonized with jazz chords and evoking Joe Williams rather than Johnny Cash. For an encore, she made Carlos Jobim’s over precious and overdone “Waters of March” sound rhythmic and righteous.

Roy Haynes until October 16 (1650 Broadway, at 51st Street, 212-582-2121).

Paula West will perform again October 14, 15, 18-22, 25-29 & November 1-5 (59 W. 44th Street, between Fifth and Sixth Avenues, 212-840-6800).