The debate rages on as to whether department stores should greet customers with “Merry Christmas” or “Happy Holidays.” I wish I could take whoever is in charge of such matters to see Feinstein’s at the Regency, where Michael Feinstein is currently presenting his annual December show, “Home for the Holidays,” and show him a perfect example of how to celebrate the season in a way that’s at once traditional and multicultural, inclusive rather than exclusive.

Mr. Feinstein’s most basic tactic is to point out that nearly all of the great Christmas songs were written by Jewish composers. This is no small matter: Even though Irving Berlin (represented by “White Christmas”) and Mitchell Parish (“Sleigh Ride”) did not grow up with Christmas, they came to understand it as well as anybody, and they were able to pour their feelings for the holiday into songs that have profoundly influenced the way subsequent generations experience Christmas. In that sense, Jewish songwriters have played a terrific role in shaping the way people around the world celebrate Christmas. Further, Parish’s text to novelty composer Raymond Scott’s “Christmas Night in Harlem”is even more remarkable in that a pair of Jewish songwriters attempted to describe how the holiday was celebrated in the most famous of black communities.

As usual, Mr. Feinstein brings total sincerity to these traditional tunes, and other non-holiday-oriented songs as well. On opening night last Tuesday, he was accompanied by his regular backup band, with musical director John Oddo alternating with Mr. Feinstein at the piano, Jay Leonhart on bass, Bucky Pizzarelli on guitar, and Mark Vinci on drums. Joining the group were the trumpeter George Rabbai (whom Woody Herman used to introduce as the “World’s only Italian Rabbi”) and the multi-reed player Dan Block, plus three backup singers (Margaret Dorn, LaTanya Hall, and Catherine Russell, who were introduced last year as “The Feintones”; this year they are “The a-Dorn-ments”).

As we have come to expect, Mr. Feinstein is at once a performer and archivist, reviving not only worthy, obscure songs, such as “Pig Foot Pete” (an Oscar contender from 1942 that lost to “White Christmas”), but vintage arrangements, such as Kay Thompson’s swinging treatment of “Jingle Bells” and a stylish chart on “That Certain Feeling,” which was written for Bob Hope.

But while Mr. Feinstein does such rhythm songs capably, and is usually backed by Mr. Oddo on these, his strength is with the classic ballads, for which he generally accompanies himself. The highlight on opening night was a semi-spontaneous, by-request medley of Gershwin classics, which he sang slowly and poignantly, with complete conviction. He was also especially moving on “Old Friend,” which seemed seasonally appropriate with its concern for relationships that somehow remain stable over the passage of time. The number has a tendency to sound rambling and tuneless when other singers do it, but Mr. Feinstein skillfully transforms it into a vivid story-song.

Talk about diversity: Mr. Feinstein’s specialty is the great book of traditional ballads from the 1940s, but one of his most effective numbers is “That’s What I Want for Christmas,” a 1966 R&B-styled hit for Nancy Wilson. “Who’d have ever thought you’d hear me with triplets?” he asked the crowd — 16th note triplet runs à la Fats Domino, at that. In a similar vein, he played “I Found My World in You,” a memorable doowoppy love song by Neil Sedaka, then invited the composer himself to take the stage. Mr. Sedaka obliged with a new song, titled “Lonely Christmas in New York,” which sounded like it could have been written in 1960, and his pop hit, “Love Will Keep Us Together.” Mr. Feinstein ended with Harold Arlen and Johnny Mercer’s depiction of a black church, “Ac-Cent-Tchu-Ate the Positive,” and, using the choir to good effect, came off like a Southern Jewish preacher.

In including some of the more suitable songs from the rock ‘n’ roll era, Mr. Feinstein is combining musical diversity with cultural diversity. I’m sure he could sing a Kwanzaa carol if he wanted to. If the singer-pianist, who is a committed vegan, can so believably tell the story of the decidedly non-kosher “Pig Foot Pete” (“Tofu Pete” somehow doesn’t work), then anything is possible.

“Home For The Holidays” runs through December 30 at Feinstein’s at the Regency. Mr. Feinstein is also appearing at the club on New Year’s Eve, but, as he announced in his show, as of December 31st “All Christmas songs are banished.”

Until then, Mr. Feinstein will have to share the city’s spotlight with some of the other premiere holiday shows around town. Here are some of the special jazz and cabaret concerts set to arrive in the coming days:

JAZZ AT LINCOLN CENTER: RED HOT HOLIDAY STOMP

Wynton Marsalis’s annual Christmas show has grown into the same kind of annual tradition that Mr. Feinstein’s has for the cabaret world. This year’s edition spotlights another star-studded lineup of Marsalis and Jazz at Lincoln Center alumni, such as Wycliffe “Pinecone” Gordon, “Warmdaddy” Anderson, Victor Goines, Joe Temperley, Reginald Veal, Herlin Riley, and the New Orleans guitarist Don Vappie. (Rose Hall, tonight and Saturday.) Mr. Temperley will also be playing at The Duke Ellington Society Christmas Party, Wednesday, December 20, at St. Peter’s.

FREDDY COLE

One artist you can always count on during the Holiday season is the venerable younger brother of the man who gave us the original “Christmas Song,” Nat King Cole. Mr. Cole is a light-fingered pianist and a nimble singer with a style all his own, who, like Tony Bennett, the object of his tribute on his new album, “Because of You,” keeps getting better as onward through the seasons we sail.

BENDING TOWARD THE LIGHT

A Nativity story at Birdland? Only if it’s the Jazz Nativity, another long-running New York City tradition. Written by singer-songwriter Ann Philliips and co-produced by her and the veteran tenor saxophonist Bob Kindred, this year’s edition stars trombonist Slide Hampton, flautist Dave Valentin, and Afro-Cuban percussion icon Candido. Also headlining this year is the Queen of Birdland herself, Hilary Kole, who will be further headlining at the club with the Chico O’Farrill Orchestra on New Year’s Eve. (Three shows, Sunday, December 24 at 6 p.m., Monday, December 25 at 5 p.m. and 8 p.m.)

MY CHRISTMAS SONG FOR YOU

In support of her spirited new album, “My Christmas Song for You,” Andrea Marcovicci hosts an all-star cabaret concert as a benefit for Symphony Space, with guests Jeff Harnar, Natalie Douglas, Barbara Brussell, Judy Butterfield (headlining the night before in the Oak Room), and Daisy Carnelia. Whether Ms. Marcovicci is singing about Santa Claus or, in her current show at the Oak Room, talking about the Incomparable Hildegarde, her great strength is her earnestness, and insatiable generosity in sharing what she loves. (December 18, at 8 p.m. at Symphony Space, Broadway at 95th Street.)

CHRISTINE EBERSOLE AND BILLY STRITCH

I’m only mentioning this Sunday evening show as a formality, because even though it has been announced as a holiday concert, I have been told that it’s already sold-out. Who wouldn’t want to see Little Edie, getting her heart broken at least twice a night (more on matinee days) from “Grey Gardens,” team up with the remarkably sophisticated singer-pianist Stritch? Sounds good to me — I’ll probably be the guy on line ahead of you. (Birdland, Sunday, December 17.)