In easily quoted turn of phrase, Duke Ellington famously described Ella Fitzgerald as “beyond category.” These two words of praise from a Duke to a First Lady have been taken by many as a Ducal denunciation of the very concept of categorization in music. Yet categories can be very useful things, and wonderful art can be created well within their boundaries: Why shouldn’t we enjoy Dixieland that’s good Dixieland, or bebop that’s good bebop?

Even so, there’s no category to which we can consign the iconoclastic trombonist Roswell Rudd, particularly when it comes to his many recordings with his frequent collaborator, the soprano saxophonist and composer Steve Lacy (1934–2004). During the course of almost 50 years, the two collaborated on dozens of projects with different kinds of ensembles. In the early 1960s, they tried, unsuccessfully, to launch a full-time working quartet (with the drummer Dennis Charles and any bassist they could get). In 1963 they recorded “School Days,” which wasn’t recognized as the classic it is today for more than a decade after it was made. Still, that seems hardly any time to wait, considering that the quartet’s first session — three songs recorded in 1962 — is only now being issued.

The original quartet disbanded when Lacy moved to Europe, but he and Mr. Rudd reunited frequently during the next four decades. The 1962 tracks provide the conclusion, appropriately enough, to a new double-CD collection of recordings by the Steve Lacy-Roswell Rudd Quartet. The set was otherwise recorded mostly in 1999, the same year Lacy and Mr. Rudd issued their well-received album “Monk’s Dream.” The new set, titled “Early and Late,” not only complements the quartet’s two other well-known albums, but is a marvelous document of the most productive off-and-on partnerships in jazz.

Throughout its long, albeit intermittent existence, the Lacy-Roswell Quartet adhered to the same constants: traditional jazz, free jazz, and Thelonious Monk. In the early parts of their careers, the two leaders were part of what was once called “the Dixieland Revival,” and both grew up in the war years wanting to play like Louis Armstrong and Sidney Bechet rather than Dizzy Gillespie and Charlie Parker. Mr. Rudd, born in 1935, attended Yale in his native Connecticut, where he played with the university’s Dixieland band, known as “Eli’s Chosen Six,” which was popular enough to record for Columbia Records. Lacy, who had already recorded with several traditional jazz and swing groups by that time, occasionally played with the Chosen Six. But by 1956, Lacy had fallen under the spell of (and begun working with) such fiercely modern pianist-composers as Gil Evans, Cecil Taylor, Herbie Nichols, and, most dramatically, Monk.

Lacy and Mr. Rudd had no qualms about moving from the Dixieland style, which, though popular, was considered by the avant-garde to be the most oldfashioned kind of jazz. Both men were helped by their choice of instruments: Lacy’s soprano saxophone had been introduced to jazz by Sidney Bechet, and essentially only played by his Dixieland disciples. The trombone had, in 30 years, evolved so far from its tailgate origins that Mr. Rudd might as well have been playing a different instrument from such trombone bop stylists as J. J. Johnson and Kai Winding. In contrast to their smooth, unblemished lines, facile technique, and lightning-fast articulation, Mr. Rudd specialized in playing the blue notes, smears, wheezes, and other vocalized inflections associated with the blues and early jazz, and simply kept on doing that as he moved from pre-modern to post-modern.

By 1999, the Lacy-Rudd foursome had perfected its free-Dixie hybrid to the point where the blend was seamless, yet never so complacent as to become a genre unto itself — as if it were even imaginable that anyone would ever follow them. In the opening “head” statements, in which the two horns play simultaneously, they utilize the essentially heterophonic lines of old New Orleans, playing roughly the same notes at the same time but looping and swirling around each other.

On the individual improvisations, however, Lacy and Mr. Rudd followed Ornette Coleman’s model: The solos spin off the melodic line rather the chord changes — bebop style. Yet what chords there are sound highly boppish, especially if one regards Monk and Nichols to be beboppers. Monk’s influence is everywhere, and even the original tunes by the two co-leaders seem to use him as a starting point. Mr. Rudd defers to traditions in the way he quotes “Chattanooga Choo Choo” and “Night Train” (something I can’t imagine Taylor or even Monk doing) in the middle of his unaccompanied solo segment in “Blinks,” while Mr. Lacy throws “I’m an Old Cowhand” into Cecil Taylor’s “Tune 2.”

At another point in “Blinks,” Mr. Rudd starts a bluesy riff and Lacy approvingly remarks, “Kid Ory! Kid Ory,” as if to summon the spirit of the pioneering New Orleans trombonist. The original melodies here are short, terse, and extremely rhythmic and Monkish, and even though the tracks are fairly long(averaging10minutesapiece), none seem self-indulgent.

Yet things do rock. The longest track is a 20-minute, Latinate original by Mr. Rudd entitled “Bamako.” Here, Mr. Rudd’s pre-composed melody and his solo are indistinguishable from each other. With his gruff, blustery tone, he sounds like a bear dancing the cha-cha.

Coincidentally, the same tune appears in a very different guise in another new release by Mr. Rudd, “El Espirito Jibaro” (Sunnyside), a collaboration with the celebrated Puerto Rican musician Victor Guillermo “Yomo” Toro. Mr. Toro plays a 10-string variation on the Spanish guitar known as the cuatro, and here these two disparate instrumentalists dive into a variety of Afro-Cuban settings and an equally wide group of Pan-American rhythms.

“Bamako” is treated here as a merengue, and given an even more danceable beat by a 14-piece salsa band. Despite all the additions, the most exciting section is a brief chorus of call-and-response between Messrs. Rudd and Toro.

What’s most rewarding about “El Espirito Jibaro” (which is dedicated to the late clarinetist Kenny Davern) is that it indicates that Mr. Rudd is continuing to find inspiring new collaborators and settings in which to play even after the death of his longtime partner. The music heard on both “Early and Late” and “El Espirito Jibaro,” is completely resistant to categorization. Here, that’s a good thing.

wfriedwald@nysun.com