It’s clear that Harry Connick Jr. has a special place in his heart for Christmas songs — he’s done numerous holiday tours, TV specials, and even wrote a Christmas musical for kids called The Happy Elf — but even he had reservations when his record label asked him to record a new Christmas album.

“My first thought was, ‘Man, I thought I sang all the songs there were to sing,’” he recalls. “But I put a list together and found out that there’s a whole lot more.”

Connick’s song wish list led to What a Night! A Christmas Album, his third holiday disc, which hits stores Tuesday. Fans can likely expect some of its songs to show up on the Ryman stage Dec. 14, when Connick brings his Holiday Celebration tour to town.

Night applies Connick’s trademark croon and big-band panache to holiday standards such as “It’s the Most Wonderful Time of the Year” and “Holly Jolly Christmas,” but it also includes a first: a duet with his 11-year-old daughter, Kate, on “Winter Wonderland.”

“That was a really wild experience, to be in the studio with your kid,” Connick says. “It was something she really wanted to do, and she actually asked me if she could do it. I thought pretty hard about it, for lots of reasons. I have pretty high musical standards, and whether she’s my kid or not, I don’t want to put something out there that’s not worthy, you know? But she was extremely serious about it, and continues to work really hard, and she did great. I was really pleased.”

Recording songs like “Winter Wonderland” required a bit of imagination on Connick’s part, as the album was actually recorded in August.

“It’s funny, it’s like doing a scene in a movie,” Connick says. “You just kind of jump in there and imagine whatever you have to imagine.”

In audience’s imaginations, Connick’s become more and more associated with the holidays over the years, and that’s a connection Connick says he can live with.

“That’s fine with me. I’m proud of everything I do. Sometimes, people don’t even know I’m a musician. They think I’m Debra Messing’s husband on Will & Grace, and they have no idea that I’m a singer and piano player. That’s the way it is. If people think of me around Christmastime — I hear it a lot, and I’m so happy to hear it. People say, ‘We always put your Christmas album on.’ It’s just a nice feeling, and I’m honored by it.”