Don Byron may not be the world’s most technically endowed clarinetist, but his 1993 album “The Music of Mickey Katz” was a watershed event in the history of Jewish jazz, doing for klezmer music what a Jewish New Yorker named Stan Getz did for bossa nova and what a black South Carolinian named Dizzy Gillespie did for Afro-Cuban jazz: They put these genres on the map by showing that they had relevance beyond the ethnic groups who created them. Mr. Byron proved that you don’t have to be Jewish to play klezmer any more than you have to be from the Mississippi Delta to play the blues.

Unlike bossa nova or Afro-Cuban music, though, there is no convenient terminology for the sounds that emerge from the melding of traditional Jewish band music and modern jazz. “Jewish jazz” and “Klezmer jazz” just don’t cut it; perhaps the best term is Mickey Katz’s “Hebop.” There is, however, an ever-increasing school of players who specialize in it, such as John Zorn, Steven Bernstein, and Paul Shapiro, not to mention the dozens of musicians who release albums on Mr. Zorn’s Tzadik label. The idea that this music is a going concern is borne out by two current releases, one newly recorded and the others from the vault.

The Russian-born saxophonist and clarinetist Alex Kontorovich’s first album, “Deep Minor” (Chamsa) is the latest of a series of attempts to fuse klezmer and jazz. Unlike, say, Brazilian jazz, in which there is an agreed-upon way to do things, everyone playing this music has to devise his own way of bringing the disparate elements together, and Mr. Kontorovich’s music ultimately doesn’t sound anything like Mr. Zorn’s or Mr. Bernstein’s. The album’s opener, “Transit Strike Blues,” begins with Mr. Kontorovich and the banjoist Brandon Seabrook playing together in approximate heterophony. The pairing may suggest Dixieland, but the riff is a complex, boppish line, and since both players use a lot of pentatonic and blue notes, the track, like much of the album, exemplifies the slogan of the Art Ensemble of Chicago: “Ancient to the Future.”

Throughout the record, a continuous attempt to mix and match various genres of jazz and world music persists. For the most part, it is organic and natural rather than forced: “Kandels Burning,” dedicated to the pioneering klezmer clarinetist Henry Kandel (1885–1943) starts as a straightforward klezmer dance number in cut time, with Mr. Kontorovich playing alto (utilizing the same off-the-map intonation as his clarinet), and building to a drum and banjo interlude that sounds more like the Bad Plus.

At times, Mr. Kontorovich seems to be pulling our leg: The piece he titles “New Orleans Funeral March” sounds nothing like a Crescent City street parade, except perhaps for the understated use of a snare drum. Rather, it sounds overwhelmingly sensual in some spots (perhaps we’re marching through the red light district), and like a chaotic combination of free jazz and heavy metal in others. Mr. Kontorovich sets “Waltz for Piazzolla” in a rough 3/4, but it’s certainly unusual to dedicate a waltz to the late Argentine master of the tango. “AfroJewban Suite” puns on Chico O’Farrill’s “Afro-Cuban Suite,” but it doesn’t contain any Latin rhythms, suggesting instead a Jewish version of Ornette Coleman’s Prime Time and Steve Coleman’s various combinations of jazz and electro-funk.

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Reboot Stereophonic (www.rebooters.net) is a nonprofit record label dedicated to illuminating neglected corners of the Jewish music tradition. Most recently, the label re-issued an obscure and extremely interesting gem from the Eisenhower era, the work of a veteran musician who is still with us. Fred Katz’s 1958 album, “Folk Songs for Far Out Folk,” may not be a lost masterpiece, but it blends traditional Jewish music with various forms of American pop in fascinating ways.

Mr. Katz — composer, educator, and jazz’s first star cellist — is one of the stranger characters in 20th-century music, although he had the distinction of collaborating with both Tony Bennett (in an army band) and Eric Dolphy (in Chico Hamilton’s Quintet) early in their respective careers. Mr. Katz had already crafted such offbeat projects as Carmen McRae’s “Carmen for Cool Ones,” perhaps the strangest jazz or pop vocal album of its day, and Ken Nordine’s “Word Jazz” series when, in 1958, he persuaded Warner Bros. to let him put together an album of treatments of what he referred to as folk songs from three traditions: African, American, and Hebrew.

Of primary interest on the record are two Hebrew tunes, “Rav’s Nigun” and “Baal Shem Tov,” that are arranged in a very busy, somewhat precious jazz-chamber style with woodwinds, and an overall sound that is similar to Mr. Katz’s writing on the Carmen McRae album. The tunes feature the major Los Angeles multi-reed virtuoso Buddy Collette, although without improvisation. The record’s four American numbers use rhythm section only, and are a direct extension of what Mr. Katz had already done for the Hamilton Quintet. The young John Williams (later of movie and Boston Pops fame), who doubles on piano and celeste, must have felt at home with this jazz-classical-pop approach, since his father was the drummer with the similarly motivated Raymond Scott Quintette 20 years earlier. If Aaron Copland had started a jazz band, this is what it would have sounded like. One gets the feeling that Warners (which assigned the veteran guitarist and big-band leader Alvino Rey to produce) went ahead with the album primarily because of Mr. Katz’s three very exciting, Kenton-esque African-styled production numbers, which were an ideal showcase for the new stereophonic process that was already selling a lot of albums in the late ’50s. Performed by a combination of six brass players (evenly divided between trumpets and trombones) and five percussionists, these three tracks anticipate what Duke Ellington would achieve a few months later with a jazz orchestra and expanded percussion on his famous “Malletoba Spank.”

These two Jewish-jazz fusions, featuring two very different instrumentalist-composers, have almost nothing in common with each other in a production sense. Taken cumulatively, though, they show that Hebop, for lack of a better word, is a music with a future as well as a past.

wfriedwald@nysun.com