Harry Connick, Jr. has been making records for 20 years now, but there are still many New Orleanians who don’t know what to make of him. In the process of conquering first the New York cabaret world, then the jazz charts, movies, TV and finally Broadway, he has been resented by a segment of the New Orleans tastemakers who have always seen him as a child of privilege. So while he has been the most visible New Orleans musician without a rival in sight the last two decades, it has often been hard to find him taken seriously in the local music print media, or on WWOZ.

At times, Connick has not helped his cause. The overt embrace of Sinatra at the beginning of his big band career (and the resulting “new Sinatra” hype) did not help him appear to be something new. The emphasis on his acting made him suspect with some musicians. His submersion around age 20 in the spiky, often bangy mannerisms of jazz pianist Thelonious Monk surely confounded those who didn’t understand why he would be interested in incorporating Monk into his piano style.

Well, it’s time for the Harry haters to get over it. HC, Jr. is making great records these days, and—for those of us who care about such things—music with a high New Orleans content.

His arrangement with Columbia has allowed him to release three albums of predominantly instrumental music on the Marsalis Music label: first Other Hours in 2003, then Occasion, a nifty collection of challenging originals with saxophonist Branford Marsalis, and this January, Chanson du Vieux Carre. There have been many attempts to meld the New Orleans trad jazz repertoire with the big band over the years, from Bob Crosby in the ’40s thru Al Hirt and Pete Fountain to Nicholas Payton and Wynton Marsalis. Chanson du Vieux Carre is as good as any of these, and better than most of them by far. Connick is an exceptional arranger with a knowledge of the whole of jazz from New Orleans forward; and his band is terrific. His piano playing is wonderful, a sly, often dissonant rejoinder to the bombast inherent in the modern big band idiom. If in the past his playing was sometimes a pastiche of James Booker, Monk, Erroll Garner and others, he has for a few years now put out something that’s truly his own.

Oh, My Nola continues the orchestral sound of Chanson, with vocals added. Connick’s singing is just fine here. The older he gets, the less Sinatraesque he becomes, and there’s some strong gospelizing here that’s far removed from Frank’s world. Songwriting has never been Connick’s greatest strength, but the originals on this disc, like the moving “All These People,” are as good as, say, any of the tunes written for The River in Reverse, the recent Allen Toussaint/Elvis Costello collaboration. As for covers such as “Sheik of Araby,” “Jambalaya” and “Bill Bailey,” you could hardly pick more hackneyed tunes, but Connick makes you snap to attention with these extravagant renditions.

Connick has really hit his stride, going back to the music of his childhood and reinterpreting it with the skills of a master arranger and pianist. His singing and songwriting get better and better. Unlike many New Orleans musicians who recycle their hits from 20 to 50 years ago, he is constantly producing new material, taking the tradition and making it contemporary. If anyone is the New Orleans musician of the moment, it is Connick.