Many of the fans who watched Sonny Rollins perform his fifth open-air concert in Damrosch Park on the Lincoln Center campus Sunday night probably did not get what they were expecting. But in this case, that is distinctly not the same thing as being disappointed.

The most memorable moments of Mr. Rollins’s outdoor performances are usually his crowd-pleasing calypsos, which typically bookend his shows. In the climactic calypso, Mr. Rollins usually gets progressively more intense and inventive during a long solo, piling on the excitement and the tension as if he were the Hitchcock of the tenor saxophone. He builds to such a peak of exhilaration that ones feels the main reason he is playing outside is because no building could possibly contain him — the power of his musical vibrations would surely reduce Avery Fisher Hall or Carnegie to a pile of debris.

Early in the evening, there was considerable tension in the crowd, which, for once, was not inspired by Mr. Rollins’s playing. An hour before the outdoor performance, it had been raining heavily, and thunderstorms were predicted for later in the evening. Thankfully, during the two hours of Mr. Rollins’s show, the rain didn’t amount to anything more than some drizzles here and there.

After nearly 60 years as a major player, Mr. Rollins has perfected a highly personal brand of jazz (with pop and heavy Afro-Caribbean elements), which begins with his band. Where the standard front line of a modern jazz group is trumpet and sax, Mr. Rollins’s co-star is trombonist Clifton Anderson (also his nephew, and the producer of his new album). He also features electric guitar (Bobby Broom) rather than piano as his customary chordal instrument, electric bass (Bob Cranshaw) instead of acoustic (except for one tune), and a two-man percussion section consisting of the fine Victor Lewis on drums and Kimati Dinizulu sporting a battery of African instruments (including apentema, apente, sankofa, kyene, djembe, and conga). With the exception of Mr. Lewis, this is the same band that performs on Mr. Rollins’s new album, “Sonny, Please,” the first release on his own label, Doxy Records.

As usual, the band began and ended with two calypsos, the new “Nice Lady” and “Don’t Stop the Carnival” (which he first recorded in 1962). Though they were almost as lively as ever, most of the highlights Sunday, surprisingly, were Mr. Rollins’s more introverted moments. The second tune was Noel Coward’s “Someday I’ll Find You,” which, as he says on his Web site, he learned not from “Private Lives,” but from the 1940s radio program, “Mr. Keene, Tracer of Lost Persons.” Mr. Rollins first recorded this waltz in an urgent, insistently hard-bop treatment in 1958, but nearly 50 years later, he played it with more worldly-wisdom and tenderness. (And that’s even though a lot of the concert performance was given over to lengthy trades with the two percussionists.)

The third tune was a fast bop blues, “Nishi,” for which Mr. Cranshaw switched to acoustic, stand-up bass. Mr. Rollins spun chorus after chorus of chordal improvisations, though “spun” is hardly the right verb for his music — these were not light, spider-webby, smoke-ringy wisps of melody, but heavy and intense musical lines, forged as if on an anvil.

The most substantial (and unexpected) new contribution to Mr. Rollins’s repertoire, both at the show and on the new album, is “Serenade.” Adapted from the 1900 ballet “Serenade Les Millions d’Arlequin” by the lesser-known Paduan composer Ricardo Drigo (born 1846), the piece was first heard as a pop song in England, played by British dance bands around the time of the composer’s death in 1930. It’s a beautiful tune and Mr. Rollins makes the most of it. Although there were solos by Messrs. Anderson and Broom, as well as an unnecessary percussion interlude, the charm here is in the pure, sonic pleasure of hearing Mr. Rollins’s deep, rich tenor tone essay this lovely line. It’s one of the most pleasing sounds in all of nature.

At this point, Mr. Rollins introduced “J.J.” (as in Johnson), the latest in his series of short, poignant dedications to fallen comrades (such as “Wynton” for Wynton Kelly and “Remembering Tommy,” for Tommy Flanagan, on the album). He played “Don’t Stop the Carnival,” but then, surprisingly, stopped the carnival well before the rabble-raising climax all were expecting.

What he did do, however, was launch into an unexpected encore: It began with “I See Your Face Before Me,” and from there launched into a glorious, unaccompanied coda, in which he played long chunks of whatever tunes he felt like. It could have been called “Oh Look at Me Now Thinking About You and the Daring Young Man on the Flying Trapeeze Singing Polly-Wolly-Doodle All the Day.” Finally, the rhythm section rejoined him on Irving Berlin’s “They Say It’s Wonderful.” If that is indeed what they say, and they are talking about Sonny Rollins, then they’re right.

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The only disappointing thing about this year’s Charlie Parker Jazz Festival, which is held every year at Marcus Garvey Park uptown and Tompkins Square Park downtown, was that the announced headliner, 85-year-old bop drummer Chico Hamilton, was in the hospital and did not appear. This weekend, the pleasant surprise came on the first day, when all the stars (who were primarily saxophonists, fittingly) went out of their way to pay homage to Charlie Parker by playing his music.

Greg Osby (alto) deftly alternated between Bird classics like”Billie’s Bounce” and “Ornithology,” as well as Monk’s “Mysterioso” and his own originals. Sonny Fortune, began with a Bird medley of mostly blues — “Barbados,” “Au Private,”and “Now’s the Time”— played on three different horns, including flute and soprano, upon which bebop and Parker’s music are rarely played. George Coleman (tenor), another blues specialist, rhapsodized over the mournful and sensual “Parker’s Mood” and burned up the air with “Cherokee.”

The wild card in the deck was the 29-year-old New Orleans pianist-singer Davell Crawford, who closed the afternoon. His incessant scatting can be a little irritating at times (like Tania Maria with hiccups), but he had done his homework and assembled an impressive program of Parker-centric music, including “Yardbird Suite.” Commemorating the anniversary of Hurricane Katrina, Mr. Crawford finished with a slow, soulful treatment of the theme song of Louis Armstrong, New Orleans’s greatest son, “When It’s Sleepy Time Down South” — an appropriate closer for a most enjoyable afternoon in Manhattan North.