When Wynton Marsalis and the Jazz at Lincoln Center Orchestra climaxed their concert Thursday night at the Rose Theater with “Rhapsody in Blue,” they were, in a very literal sense, settling an old score. The last time the JALCO played the “Rhapsody” was in November, at an all-Gershwin Gala. That treatment featured the pianist Marcus Roberts as star soloist, but, through no fault of the orchestra or Mr. Roberts, it had to be the worst version of Gershwin’s classic that I’ve ever heard.

The problem was not that Mr. Roberts chose to improvise the famous piano solo (rather than playing what Gershwin wrote), but the actual orchestration. This was simply the most bowdlerized, bastardized, heavy-handed, misguided deconstruction of the “Rhapsody” imaginable — it could have been arranged by Fred Flinstone.

That night, the “Rhapsody” ruined what was an otherwise fine concert; on Thursday, it provided a fitting climax for one. This weekend’s “Rhapsody” was a tidy, fiveminute reimagining commissioned by Duke Ellington from Billy Strayhorn in 1962 for an album called “Will the Big Bands Ever Come Back?” (and transcribed for the JALCO by David Berger). Strayhorn’s treatment is notable for the way it retains the majesty of the 1924 original while changing nearly everything about it, starting with the famous introductory clarinet glissando, now played on gliss-less baritone saxophone (Joe Temperley), to the piano part (Dan Nimmer), rendered in Ducal keyboard terms, and building to a romantic tenor saxophone part and a reed coda in which alto (Sherman Irby) and clarinet (Victor Goines) intertwine, letting the clarinet have the last word rather than the first.

The last few big concerts by Jazz at Lincoln Center have, to its credit, featured mainly new and, in some cases, very challenging music. This weekend’s show, “The Songs We Love,” was a welcome visit with some old friends. Some of these, songs, like the Count Basie-Wild Bill Davison arrangement of “April in Paris”and Dizzy Gillespie’s chart on his own “Night in Tunisia,” were so well-worn that the Lincoln Centurians could have easily read them down “cold” onstage without a single rehearsal. Other pieces, like the Ellington-Strayhorn “Rhapsody” and Oliver Nelson’s recasting of the spiritual “Down by the Riverside” (originally written for Jimmy Smith and Wes Montgomery but here played without organ or guitar), showed that you can still be surprised by an old friend.

The evening was not only a tribute to the A-list composers of the Great American Songbook but, naturally, to the great orchestral jazz arrangers: Don Redman was represented by his gently swinging 1932 treatment of “Tea for Two” and Benny Carter was done yeoman service by the JALCO’s fiveman reed section, which got every nuance of phrasing and dynamics right on Carter’s masterful “All of Me” — something that they did have to rehearse. I was disappointed with the absence of any Sy Oliver or Gil Evans, but I was especially glad to hear Bill Russo’s swinging, thoughtful treatment of “Fascinating Rhythm” (when is the JALCO going to give us an all-Stan Kenton concert?) and also the John Kirby version of “Sweet Georgia Brown,” in which Mr. Marsalis played Charlie Shaver’s arrangement and trumpet solo in the original’s mega-fast tempo.

Mr. Marsalis also excelled in a pointillist treatment of “Stardust,” in which the melody was broken down into four-bar chunks and spread among the horns — an ensemble arrangement with almost no ensemble playing. Joe Temperley delivered what might have been my favorite solo of the evening on Gerry Mulligan’s abstract yet uncompromisingly warm and romantic take on “My Funny Valentine.” The other star of the evening was the pianist Dan Nimmer, who showcased his knowledge of classic keyboard styles; I haven’t heard anyone his age “do” Earl Hines in quite a while. (At 25, he’s a young “Fatha.”) This current rhythm section, which co-stars the bassist Carlos Henriquez and the drummer Ali Jackson, has been jelling quite well in the 18 or so months that it has done double duty with the JALCO and Mr. Marsalis’s own group.

On the whole, the Lincoln Center Jazz Orchestra proved that you don’t need to push the envelope or run to the fringe to produce an evening of exciting music. And producers take note — just like any event at the JVC Jazz Festival or the 92nd Street Y that combines jazz with the Great American Songbook, it was completely sold out.

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The pianist Bill Charlap told me recently that he defines the term “jazz repertory” quite literally: For him it means to take a classic performance and re-create it note for note, down to the solos themselves. With “The Birth of Cool,” presented in the Allen Room in four performances on Friday and Saturday, Mr. Charlap didn’t recreate anything that specifically, but instead offered the musical equivalent of a 90-minute essay on the origins and development of the cool side of jazz.

Mr. Charlap began with his regular trio — with Peter Washington on bass and Kenny Washington on drums — to which he added an allstar lineup of seven trumpeters and saxophonists (plus the guitarist Gene Bertoncini and the singer Mary Stallings), broken down into different combinations. Regrouping with almost every number, Mr. Charlap explored the nature of jazz coolness from Lester Young and Count Basie to Claude Thornhill, Lennie Tristano, Miles Davis, Gerry Mulligan, and even Igor Stravinsky.

It was an ambitious task to chart the course of cool through roughly 15 eventful years, hitting all the major soloists and ensembles, from Basie’s All-American rhythm section to Tristano’s two-sax quintet to Mulligan’s piano-less quartet. He also offered his own new reworking of Gershwin’s “A Foggy Day,” which recaptured both Thornhill’s Orchestra and the 1949 Davis “Tuba” Band (without tuba).

The lynch pins of the presentation were two very different readings of the standard “Pennies From Heaven,” first as rendered in the style of Billie Holiday and Lester Young by the excellent Ms. Stallings and the increasingly legendary tenor Frank Wess, in more or less the original major key. He returned to “Pennies” as re-rendered by Tristano in the variation variously labeled “Lennie’s Pennies” or “Pennies in Minor.”

I don’t think I’ve ever heard anyone reconstruct the classic Tristano quintet before, with its famous front line of tenor saxist Warne Marsh (Mark Turner) and alto saxist Lee Konitz (Jon Gordon). Here, Mr. Charlap showed, as the Orchestra did with Kenton, that Tristano’s music ought to be heard within the walls of JALC’s Rose Hall more often.

By coincidence, Mr. Charlap’s concert also included the music of Gerry Mulligan, whose baritone part on “Line for Lyons” and “A Ballad” was essayed by the terrific multireed virtuoso Scott Robinson, while Warren Vache was also outstanding playing muted on the opener “Oh, Lady Be Good” and evoking Roy Eldridge on “I Can’t Believe That You’re in Love With Me.”

As satisfying as it was, an hour and a half is hardly time to do justice to a strain of jazz that runs through the whole history of the music. I look forward to a second installment that will go back to Bix Beiderbecke and forward to the Modern Jazz Quartet. This weekend’s concert was a sweet beginning.

wfriedwald@nysun.com