It seems fitting that in the first year after the great flood in New Orleans, New York’s two major jazz festivals return to the roots of the music by kicking off with parades.

The JVC Jazz Festival, as usual, got underway with a picnic-style reception at Gracie Mansion, but this year the featured act was the Preservation Hall Jazz Band, which has been the flagship band of New Orleans jazz for four decades; their set on Monday concluded with a parade around the picnic grounds. The following evening, the 11th annual Vision Festival began with an “opening invocation” in which four performers proceeded up the center aisle of the Angel-Orensanz Foundation, the former synagogue in which Vision is staged. The saints had now come marching in.

Vision’s onstage festivities opened with the Raphe Malik Tribute Band, a septet led by the tenor saxophonist Sabir Mateen and featuring Jemeel Mondoc (alto sax), Roy Campbell and Lewis Barnes (trumpets), Dave Burrell (piano), Warren Smith (drums), and one of the festival’s organizers, William Parker (bass).The band honored Malik, a free-jazz trumpeter and Vision mainstay who died in March at 57, by playing his music. What made it interesting was that most of these compositions were written spontaneously, and the group learned them by listening to tapes of Malik’s performances, mostly at the 2003 Vision Festival.

These tunes were mostly short lines with long improvisations.Thanks largely to the dependable Messrs. Parker and Smith, the free-wheeling improvisations of Mr. Burell and the horns were well-grounded. Even when the saxophones and trumpets accompanied screams in the foreground with screams in the background, the bass and drums always gave you something to hold onto, a rhythmic anchor, so that you never got completely lost in the improvisations.

The most ambitious work compositionally was Mr. Smith’s “A Toast to Raphe,” which had the kind of complex,multi-strain structure – complete with changing tempos and time signatures – that one rarely finds in free jazz. The piece even had an intro in 3/4 time, before moving into a standard four, and seemed fully coherent even when the four horns approximated a charging herd of rhinos.

Though Vision primarily presents postmodern jazzmen associated with New York’s Downtown scene, the organizers also bring in experimental musicians from all over the world. Following the Malik tribute on Tuesday evening was the Dutch Klaas Hekman, who plays the rarest of all saxophones, the gigantic B-flat bass saxophone.

This unwieldy horn is generally used in 1920s jazz recreations (by Vince Giordano and Scott Robinson, for example) but here Mr. Hekman played avant-garde jazz chamber music in a trio with cello (Fred Lonberg-Holm) and piano (Veryan Weston). Drawing on both American and European traditions, Mr. Hekman alternated between a starring solo role, and that of an accompanist, playing a walking bass line on his mega-sax.

The third act on opening night was an extremely free quartet featuring pianist Borah Bergman, alto saxophonist Louis Belogenis, Mr. Parker on bass, and Rashied Ali, the famous drummer from John Coltrane’s last group. The quartet’s 50-minute set consisted of one uninterrupted tune in which the four men constantly regrouped into different combinations. Mr. Parker and Mr. Ali provided a rock-solid foundation while Mr. Bergman headed off into outer space with Mr. Belogenis – the latter frequently contorting his body as if he were the Keith Jarrett of the sax.

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Up at the Kaye Playhouse, the JVC Festival staged a “Tenors Galore” program on Wednesday evening. The first half starred the forceful tenor saxophonist Eric Alexander with his quartet of pianist Harold Mabern, bassist John Webber, and drummer Joe Farnsworth and, as a special guest, the equally remarkable tenor Harry Allen.

The bulk of this set was taken up with a two-tenor joust in the tradition of Zoot Sims and Al Cohn. For his featured solo with the rhythm section, Mr. Allen played a highly expressive ballad, Gershwin’s “How Long Has This Been Going On?” with an unaccompanied verse and closing cadenza, as well as lots of vibrato and very breathy exhalations on nearly every note – all of which combined to make the sound all the more tender and vulnerable. Of the two, Mr. Alexander is a player with formidable technique and perhaps a broader, more modern command of harmonies, but to me, no one plays with more emotional resonance and just plain wallop than Harry Allen.

For the second half, Houston Person, who, at 71, is one of the great living heirs to Coleman Hawkins and Ben Webster, took over with his quartet of pianist Stan Hope, bassist Per-Ola Gadd, and drummer Chip White. Playing ballads (“Too Late Now”), burners (“Lester Leaps In”), boppers (“Social Call”), and the blues (“Please Send Me Someone To Love”), he played a competent and frequently inspired set that showed he doesn’t even have to work up a sweat to be impressive.

I was momentarily disappointed when I realized that Messrs. Alexander and Allen weren’t going to come out and join Mr. Person for a three-tenor climax, but Mr. Person compensated with a soulful reading of “The Way We Were.” This was the first time I have ever enjoyed listening to that over-baked 1970s pop anthem.

The Vision Festival runs until June 18 at the Angel Orensanz Foundation For The Arts (172 Norfolk Street at Houston Street). JVC Jazz Festival runs until June 24 at various locations. For more information, visit www.visionfestival.org and www.festivalproductions.net.