Louis Armstrong’s position in jazz may be, in Dizzy Gillespie’s famous phrase, “unimpeachable,” but there was a moment when, in the radical 1960s, Armstrong was actually denounced by some younger musicians — not for his music, but for his comedy and crowd-pleasing stage antics. The trumpeter Jimmy Owens, however, was one contemporary jazzman smart enough to see through the act. Once, at a concert during this period, my father commended Mr. Owens for his pro-Satchmo position, and the musician responded: “Louis Armstrong was never Uncle Tom to anybody who played the trumpet.”

Since that time, few musicians — and virtually no trumpeters — would dispute that Armstrong remains the most essential figure in all of jazz. Most of the time, his memory is honored by traditional and swing players (such as the Armstrong Centennial Band, which, after nearly a decade, continues to play Wednesday evenings at Birdland). But modernists and even avant-gardists owe him just as much. It was particularly satisfying, then, to see the Festival of New Trumpet Music, the annual series mounted by the trumpeter-composer-bandleader Dave Douglas, begin its sixth year on Sunday with a salute to Satchmo staged at the man’s own house in Corona, Queens.

By a welcome coincidence, the following night the Sidney Bechet Society held one of its own concerts in honor of the organization’s namesake, who was Armstrong’s contemporary, occasional collaborator, and near-equal as a founding father of jazz.

Jimmy Owens was in attendance on Sunday at the Armstrong house; he could have just as easily been in the band, but the music was in the capable hands of Eddie Allen, who, among many other things, teaches at Brooklyn College and is the regular trumpeter with the tuba player Bob Stewart’s brass-centric quintet. For the group, which he called 3hree for Louis, Mr. Allen recruited two other versatile trumpeters: the much-storied Cecil Bridgewater and the prodigious James Zoller. (The rhythm section consisted of Bruce Barth on piano, Kenny Davis on bass, and Jerome Jennings on drums).

Mr. Allen’s approach was to take 18 songs associated with Armstrong and arrange them in new treatments for the three-trumpet, three-rhythm ensemble. By “new treatments,” he principally meant giving the tunes a modern feel and new rhythms. “West End Blues” began the afternoon with Armstrong’s classic opening cadenza, but then pushed the melody against a strong Latin backbeat.

A recurring gambit during the performance was to take familiar tunes and mold them into unusual time signatures: “On the Sunny Side of the Street” and “Rockin’ Chair” were both in 3/4 time (the former as a modal waltz), “Ain’t Misbehavin'” was in 5/4, and “All of Me” was in 7/4, making for a veritable blue rondo. There was also a hard-boppish “Struttin’ With Some Barbecue” and a cha-cha-cha on “Mack the Knife.”

Although some of the arrangements got a bit precious at times, and possibly a bit tricky just for the sake of it, the tribute to Armstrong was a worthy project that Mr. Allen should consider developing into an album. Mr. Bridgewater played a pointillistic statement on “Ain’t Misbehavin’,” crafting a distinct melody from as few notes as possible. For Armstrong’s theme song, “When It’s Sleepy Time Down South,” Mr. Zollar permitted himself the luxury of an outright Satchmo imitation; we’ve heard people mimic his vocalizing and his open-bell tone on trumpet, but Mr. Zollar did a remarkable job of capturing Armstrong’s muted sound, which the master often employed when accompanying singers.

The show closed with “Do You Know What It Means to Miss New Orleans,” which was reconstructed as a Crescent City parade march, and “What a Wonderful World,” set to a rocking dance beat. Normally at such a tribute, one would be tempted to say that, somewhere, Louis Armstrong was looking down and smiling. But since the musicians happened to be playing just a few feet from where Satchmo’s spirit resides, everyone in attendance knew that he was right there with us.

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The concerts by the New Orleans clarinetist Evan Christopher have become an annual event for the Sidney Bechet Society, which is to be commended for its imagination. Other than playing the same instrument and residing in the city of the pioneering reed-giant’s birth, Mr. Christopher has nothing in common with the late Bechet (1897-1959). Rather than a Bechet disciple (such as Bob Wilber, who played for the SBS in June), Mr. Christopher is a traditional jazz counterpart to the modernist clarinetist Don Byron, in that his music isn’t focused specifically on the quality of his own playing, but rather the fascinating content of the bands he assembles and the concepts that drive them.

Almost since Bechet’s time, the clarinet has been the most classically focused of jazz instruments, and the major clarinet modernists (namely Buddy DeFranco and Eddie Daniels) have perfected a flawless, almost Mozartian purity of tone. Contrastingly, Mr. Christopher is a much rougher, more passionate stylist, influenced by the great Caribbean reed masters. He leans predominantly to the folk heritage of the instrument, and would have been right at home during the so-called New Orleans “revival” of the 1940s.

Too many traditional jazz concerts are mere marathon jam sessions on familiar warhorses. On Monday, Mr. Christopher mounted a well-conceived show built around an equally unique ensemble, combining his clarinet with the outstanding trumpeter Jon-Erik Kellso, bassist Sebastien Girardot, and two guitarists, Matt Munisteri and Pete Smith. Using the material from his recently released album, “Django a la Creole,” Mr. Christopher explored Franco-American connections in jazz through the focal point of two remarkable meetings in 1939: Sidney Bechet and the pianist Jelly Roll Morton in New York, and Duke Ellington and Django Reinhardt in Paris.

Messrs. Evans and Kellso began with a minor dirge that served as an introduction to the jaunty parade march “High Society” — as if they wanted to encapsulate the New Orleans funeral experience into a single piece. (Mr. Christopher said it was dedicated to the recent events of Wall Street, which inspired more moans than laughs.) They also treated the crowd to a marvelously Pan-American expansion of Morton’s Latin-tinged “Mama Nita,” a Spanglish soufflé that was at once a tango and a calypso, as well as an introspective revamp of Reinhardt’s reckless swinger “Douce Ambiance.”

Mr. Kellso’s solos on “Buddy Bolden’s Blues” and Rex Stewart’s “Low Cotton” showed why he is one of those masters of traditional styles who has the capacity to transcend the genre. Where some brassmen vary their approach by switching between trumpet and flügelhorn, Mr. Kellso employs a veritable painter’s palette of mutes (consisting of everything from cloth to rubber to metal) that make him sound as though he’s playing at least five different instruments. He’s such an eloquent and expressive player on the horn that I’ll be disappointed if, next year, he isn’t invited to play in the Festival of New Trumpet Music.

wfriedwald@nysun.com