New York jazz in the 1990s spawned some monstrously good working bands, outfits so keenly focused that they could trigger the transcendental glimmer of highly skilled players in burning improvisatory flux. Depending on your taste, those bands could have been Joshua Redman’s quartet with pianist Brad Mehldau, John Zorn’s all-star group Masada, the David S. Ware Quartet, or Bloodcount, which was formed by the alto saxophonist Tim Berne in 1992.

Bloodcount, which featured Jim Black on drums, Michael Formanek on bass, and Chris Speed on a second alto, was a percolating laboratory for Mr. Berne’s complex and detailed compositions. It wasn’t unusual for a Bloodcount piece to last a half-hour. If the notion implied high-minded severity, that was never the case in practice. Even at its gnarliest, the music conveyed a sense of adventure and risk, rewarding attentive ears with intriguing structures, surprising depths of soul, and spirited interactions between the players, whose roles might revolve like a Calder mobile.

“I always find that people like my bands a lot more after I stop doing it,” Mr. Berne said in his home in Park Slope, where he has lived since the 1980s. (“The downtown scene?,” he said, as if cocking an eyebrow. “I’m a Brooklyn guy.”) “But if something becomes successful, I move on and see if I can work something else out. Once it gets to the point that no one is complaining, I get nervous.”

That explains why he broke up Bloodcount in 1999. After what he cautiously estimated as a “billion” gigs, Mr. Berne, now 53, said he could no longer compose for the band’s instrumentation. But nearly a decade later, he has begun hearing some different music for the same group, and Bloodcount will mark its return to the stage Sunday at Joe’s Pub, where the 6-foot-4-inch Mr. Berne will likely play in his stockinged feet, avant-casual.

“You can reinvent an old band by writing new stuff and starting fresh,” he explained. “I didn’t want to do it as a retrospective.” For that, fans and curious newcomers can check out “Seconds,” a new CD-DVD release on Mr. Berne’s Screwgun label featuring two discs of vintage Bloodcount live recordings and a 1994 concert video from Paris. The video was shot by Susanna Schonberg and reflects the energies of the performance in a restless montage of extreme close-ups and offstage passages.

But the music Bloodcount has now begun to play sounds much different than that, Mr. Berne promised. “My writing changed a lot when I started writing for keyboards,” he said, referring to an ongoing affiliation with the pianist and electronic composer Craig Taborn, who plays in Mr. Berne’s trio Hard Cell and alongside him in a quartet with the guitarist David Torn. “There’s certain rhythmic stuff, certain harmonies, I guess rhythmically more than anything, and the counterpoint is stranger.”

Mr. Berne was a late bloomer musically. He didn’t pick up a horn until he was 19 or 20, when he got excited at the countless gigs he attended at such bustling mid-1970s haunts as Studio Rivbea and Slug’s. One day he sprained his ankle and purchased a $200 alto saxophone to help him kill time. His astute taste in mentors proved exceptionally fortunate. Mr. Berne’s favorite musician was Julius Hemphill, the visionary saxophonist and composer (“Dogon, A.D.,” “Long Tongues”), who proved amenable to taking on a completely green student.

“I started making music because I saw him doing it,” Mr. Berne said. “I was pretty naïve for quite a long time. I started as a bandleader by default. It’s a good thing I learned how to do it early on, and I learned how to put out records. I just had to learn music.” The saxophonist honed his chops and struck a deal with Columbia Records in 1986, even though he was working a much different line than the label’s loudly touted jazz star, Wynton Marsalis. The deal only lasted for two albums, but Mr. Berne became fast friends with the label’s graphic designer, Stephen Byram, and the two began a long artistic partnership. (Mr. Byram creates all of the amusingly abstract designs for the saxophonist’s CDs, which upend the dry and amateurish norm for avant-garde jazz packaging.)

“I just want to own the stuff; I don’t know if it makes any difference,” Mr. Berne said. He’s been marketing his own discs since 1996, with 19 titles available on his Web site (screwgunrecords.com). During a short spell a few years ago, he became ambitious about running an indie label, but burned out on the effort involved. Lately, he’s tried to take advantage of MP3 technology.

“Today I sold six downloads!” he said, with an air of mock pride. More common, he lamented, was learning how easily his performances could be acquired elsewhere. “It’s hard to sell stuff because everyone gets it for free. I was talking to a friend in Europe after we did some shows in Barcelona and Budapest, and he had already listened to the gig, 24 hours after we played it.”

As for the recharged Bloodcount, Mr. Berne advised to expect the unexpected. His recent European tour with Mr. Torn, whose music is dense and boiling, yielded precisely the response on which he thrives. “About 20% of the audience was shocked,” he said. “We weren’t preaching to the choir. Some like you and some don’t, and you get a kind of tension. That first year or two with a band is really different than the rest of the time. Nobody knows the music — including me.”

Perhaps the only thing for certain is that Mr. Berne’s new pieces will stretch out at their leisure. There’s a good reason he prefers extended compositions.

“I never liked to talk.”

Bloodcount performs at 7:30 p.m. Sunday at Joe’s Pub (425 Lafayette St., between East 4th Street and Astor Place, 212-254-1263).