Even in a big city filled with big bands, David Berger is unique among bandleaders. Like the Lincoln Center Jazz Orchestra and others, Mr. Berger’s band, the Sultans of Swing, can play a Duke Ellington classic exactly the way Ellington played it, and they excel at digging up obscure gems. But it is the leader’s first-rate arrangements and compositions that stand out: Mr. Berger’s specialty is writing works that so completely capture the styles of the Old Masters that you are left scratching your head and wondering if you heard them before.

This week at Birdland, Mr. Berger’s band played the second in a series of Tuesday night performances, taking over the slot recently occupied by the official Duke Ellington Orchestra. Operated by Ellington’s grandson, Paul, the latter-day Duke band wasn’t particularly good, and Mr. Berger’s men play Ellington’s music with considerably more accuracy and energy. While Ellington’s music occupied a prominent part of both of the first two weeks, Mr. Berger began and ended the opening set with Count Basie.

Well, not exactly. Though the set did end with a Basie groove on the blues, Quincy Jones’s 1958 “Rat Race,” Mr. Berger in fact opened with an original called “Stomping on a Riff,” from the band’s new album. This tune is so solidly in the Basie style that I fully expected to see the corpulent Count at the keyboard.In Basie fashion, it begins with an interlude led by the piano and rhythm section (in which bassist Dennis Irwin did double work to compensate for the absence of a rhythm guitarist), boasts an ecstatic shout chorus, and features a wailing saxophone solo, performed at Birdland by the guest star and one-time Basie sideman Jerry Dodgion.

Next up was a slow and soulful treatment of President Franklin Roosevelt’s campaign theme “Happy Days Are Here Again,” done in a hip two-beat reminiscent of Jimmie Lunceford. Dramatic breaks led into another fine solo from Mr. Dodgion.

There were essentially only two Ellington instrumentals in Tuesday’s early show, and neither of them was pure Duke. “Boo-Dah,” composed by Ellington’s partner, Billy Strayhorn, wasn’t treated to an official studio recording until after the composer’s death. The band played this typically silky Strayhorn riff with characteristic smoothness and drive.

Then came “Good and Tight,” which was an unfinished manuscript discovered by Annie Kuebler, keeper of the Ellington archives at the Library of Congress; Ellington wrote roughly half the chart, a bluesy tune but in song form with a bridge, in 1945, and Mr. Berger recently completed and titled it. Mr. Berger’s ending, which heads upward to a high-note trumpet solo and quotes briefly from “What Am I Here For,”is almost more Ellington than Ellington.

Two very different treatments of familiar standards followed. “Stardust” was rearranged as a trumpet solo for Michael Rodriguez, and both he and the band called to mind the overall sound of Clifford Brown’s famous album with string accompaniment. “It’s the Talk of the Town,”done in the style of such mid-1950s hits as “Tea for Two Cha Cha Cha,” was a brilliant illustration of Mr. Berger’s antic wit at its most droll. The band deliberately subverted the original meaning from a classic torch song into a goofy pop-mambo that featured paraphrases of the Mexican classic “Besame Mucho,” a noisy trade of phrases by the trombone section, and a stoptime unison grunt a la Perez Prado.

Mr. Berger also performed a Swedish folk song in swing time and “The Tennessee Waltz” in a solid four. Then the band’s vocalist, Jennifer Sanon, took center stage for the Glenn Miller hit turned soul standard “At Last.” Ms. Sanon is a New School undergraduate — I’m sure Mr. Dodgion has reeds older than she is — with a fantastic instrument and a breathtaking sound, but has not yet mastered the art of connecting with a lyric and an audience.

During Ms. Sanon’s second song, “I’m Beginning To See the Light,” I had a hard time believing she knew what it meant to “make love by candle shine.” But Ellington wrote a repertory of works in which the female voice is used instrumentally, and Ms. Sanon could be awesome on such works as “Creole Love Call” and “On a Turquoise Cloud.” Sweet are the uses of tradition.

July 25 and August 1, 8, 15 & 29 (315 W. 44th Street, between Eighth and Ninth Avenues, 212-581-3080).