In 1940, the pioneering tenor saxophonist Bud Freeman launched his own ensemble, which he called the Summa Cum Laude Band. The idea was similar to the one that drove the rock supergroups of the late 1960s, like Crosby, Stills, Nash, and Young: Established players who had already distinguished themselves in famous bands would get together and form an even greater unit.

That’s what bassist Gary Peacock and drummer Paul Motian are doing this week at Birdland, along with the fine pianist Marc Copland. Although Messrs. Peacock and Motian have worked together on occasion, they are best known for serving key roles in two of the most influential piano threesomes of the last half-century. Since 1983, Mr. Peacock has been a member of Keith Jarrett’s most essential band, the Standards Trio; Mr. Motian was a crucial member of the groundbreaking Bill Evans trio during its existence from 1959 to 1961. But their current trio, under Mr. Peacock’s leadership, is vastly different from both of those legendary groups – and from most other trios you’re likely to hear.

That became clear immediately as Mr. Peacock opened Wednesday’s early set by playing the melody line of Sonny Rollins’s standard “Doxy.” The bassist did what a horn or a piano usually does in a jazz combo, stating the tune and then improvising on it. When Messrs. Peacock and Motian played in the Jarrett and Evans trios, they helped set new standards for interplay among musicians, so it’s only natural that the driving idea behind the new trio would be neither groove nor melody but the ways in which three musicians can interact without any one of them subordinating the other two into a sideman role. None of the solos went on for too long, or were so assertive that you forgot the other two men were still playing.

After the bouncy “Doxy,” most of the set was dark and minor and slow, particularly the third tune, Mr. Copland’s “At Night,” which resembled a blues in format and harmony but was classical in its texture. This was Mr. Copland’s most extended feature, and I couldn’t help but think what an effort it must have been for him to not sound like Evans or Mr. Jarrett.

The fourth piece was also dark, but seemed to have no pre-set melody. For the most part, this was pure improvisation – each of the three players skittered and scattered this way and that, with even more interplay between them than usual.

It was moving stuff, but the trio then lightened the mood with a pair of standards. On the slow and stately “But Beautiful,” Mr. Copland stated the melody and Mr. Peacock responded, not simply supporting him with the chordal accompaniment typically expected of a bassist, but with a whole other countermelody in the style of Scott LaFaro. Hearing this trio play a familiar tune is particularly rewarding; you know they’ll eventually get from point A to point B, but you listen closely to discover how they’re going to get there.

The last piece began with what seemed like another themeless improvisation, but it eventually took the shape of “Takin’ a Chance on Love.” When Mr. Peacock finally got around to playing Vernon Duke’s melody on the bass, he did it very slowly and cautiously – as if to illustrate the element of risk in the lyric – but gradually gained confidence and momentum. Surely this is a trio that knows all about taking chances.

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It seems that more and more Broadway stars doing one-man shows in cabaret rooms are consciously avoiding singing songs from musical comedy. James Naughton, who is concluding a two-week run at Feinstein’s this weekend, apparently feels no need to show you what a great Broadway baritone he is – his several Tony Awards have already made that case for him. Instead, he assumes virtually every other kind of male singing role: crooner, cowboy, saloon singer, blues belter, and rocker.

Still, the most moving part of the opening night’s show was a subset of songs by the late Cy Coleman, who also blurred the boundaries between Broadway, pop, and jazz. “Real Live Girl” is a simple and direct waltz, enlivened by a key change, while the reflective “Why Try To Change Me Now” shows that, like the best actor-singers, Mr. Naughton is a master at changing personas with every song. “Everybody Today Is Turnin’ On,” a comedy song from “I Love My Wife” (Mr. Naughton’s first Broadway musical), is a brilliant 1970s-style delineation of new social mores like recreational drugs, made even funnier because it is set to an old-fashioned, vaudeville-style tune.

Shifting into folk-pop mode, Mr. Naughton was both sincere and funny on Randy Newman’s “Shame,” and on Tom Waits’s “Looking for the Heart of Saturday Night.” He then caught his audience off-guard with his encore piece, a doo-wop medley in which he sang the bass lines of a dozen late-1950s hits (that’s a lot of rama-lamading-dong), and ended in falsetto.

Peacock until June 10 (315 W. 44th Street, between Eighth and Ninth Avenues, 212-581-3080). Naughton until June 10 (540 Park Avenue, at 61st Street, 212-339-4095).