“It’s my favorite room in New York,” said jazz singer Jessica Molaskey of the Algonquin Hotel’s Oak Room, which she will play tonight for the first time. “There’s something about the literary history of it. Smart girls, you know.”

She must be thick in the rehearsal process, then, polishing her act to an Algonquin-worthy sheen. “No. They don’t rehearse,” she said with a smile and a what-can-you-do shrug. “They” are her backup musicians, who include renowned jazz guitarist John Pizzarelli and bassist Martin Pizzarelli. She’s been married to John since 1998, making Martin her brother-in-law, and their paterfamilias, music legend Bucky Pizzarelli, her father-in-law.

“They’re jazz musicians,” she explained. “They think rehearsing is like diminishing returns. Five years ago, the idea of not getting rehearsals for this Algonquin thing – I’d be throwing up right now. That part I’ve gotten used to. It used to freak me out. We just did Jonathan Schwartz’s Christmas show on WNYC, which is four hours of live music. Jonathan will say, ‘Sing, um, this.’ And all the other guys get up and go ‘Okay.’ I’m just learning to do that.”

Her home-schooling’s paid off. “Make Believe,” her third album in as many years, was released in late 2004 to grateful reviews. Ms. Molaskey is now routinely ranked by critics as one of the few contemporary vocalists who can find the heart and wit of a standard. Her evident skill with immortal tunes and bygone singing styles has elicited the inevitable comparisons.

“Sometimes people say Peggy Lee and that blows my mind,” she marveled. “The thing I love about Peggy is she sang in time and she sang in tune. She didn’t muck about with the melody. She sang the song. I try to do that. I don’t do any scatting. Irish girls from Connecticut should never scat.”

This Irish girl from Connecticut spent the first 20 years of her adult life chasing a living in the Broadway musical community, collecting mainly small roles in big musicals like “Crazy for You” and “The Who’s Tommy.” Life took a detour with the short-lived but (for Ms. Molaskey) fateful 1997 Johnny Mercer revue “Dream,” which starred John Pizzarelli. She sang “Skylark” in the show. He protectively plucked strings behind her. A baby, Madeleine, was born soon after, then a marriage, then a second career. It was Mr. Pizzarelli who first suggested she sing with his trio.

“I said ‘You’ve got to be kidding me.’ Have you seen John live? What he does is so phenomenal and unique. But for some reason the guy from Feinstein’s at the Regency wanted it to be something different than what he’d been doing with the family. That opening night was the most scared I’d ever been. Not only was I just standing there being me without a wig or a character, everyone is this far away from you. And it was my father-in-law, who just yells at you: ‘Ach! Don’t do it in that key!’ And then my husband! So the first two nights I was a wreck. And then what happened is I’d say something silly and John would make me laugh. And then we started having fun.”

Though the impish Mr. Pizzarelli is a notorious cut-up on stage, his wife is craving a little less scene stealing at the Oak Room. “He promises he’s not even going to speak,” she said, sounding doubtful. “We should have a sort of swear jar on the piano, to see how often he tries to take over. It’s really hard for him not to. He’s a vaudevillian.”

Ms. Molaskey and the three Pizzarellis have become so notorious for their the-family-that-plays-together ethos that they’ve earned an eminently marquee-able moniker: The First Family of Cool. New York Times cabaret critic Stephen Holden coined the phrase and publicists have tirelessly advanced it ever since. On the day of our interview, the Queen of Cool was wearing a comfortable outfit of black slacks and a pink top. The face is as always: a curiously fetching alliance of high cheekbones, long birdlike nose, almond shaped, exotically tilted hazel eyes, and a self-effacing, “Who, me?” grin.

“It’s so queer,” tittered Ms. Molaskey. “We end up getting into Cincinnati and there are these big posters: ‘The First Family of Cool.’ I can assure you that we are anything but. Especially my husband. He’s a big puppy dog. He’s so not cool.” She erupts into a peal of giddy laughter painfully familiar to husbands the world over.

Ms. Molaskey does not regret one whit being dragged into her paramour’s jazz world. For one thing, the welcome has been a damn sight warmer than that she’s received in the theater, where the 43-year-old most recently auditioned to play the mother of 36-year-old Hugh Jackman in “The Boy From Oz” – and didn’t get the part. “I’m quirky. Some people don’t know if I’m pretty, or funny looking, or funny or serious. So whatever. One of these days I’ll figure it out.” Her most recently theater job was in the 2002 Lincoln Center Theater musical “A Man of No Importance.” Despite the fact that her stage time was minimal, New York critic John Simon felt compelled to write, “Jessica Molaskey proves how overdue a juicy Broadway lead is for her manifest talent.”

“What was that about?” wondered Ms. Molaskey aloud. “When your reviewers get frustrated about your career, maybe it’s just time to get out. It’s so crazy, all this, after banging my head against the wall trying to do Broadway shows for so many years. It’s like every once in a while you do something and it’s easy, and it has this sort of life.”

Otherwise, Ms. Molaskey doesn’t consider the times we’re living through particularly easy ones. Certainly, they lack the sophistication and elegance she and the Pizzarellis can bring to a room. “I was watching ‘To Tell the Truth’ on the Game Show Network,” she related. “Kitty Carlisle Hart and Arlene Francis. The way they speak to one another! I find it so disturbing the way we approach one another today. I think it’s important how we speak, that we don’t dismiss people’s art just like that. The world’s coarse and a little bit mean these days. Great music reminds us of each other, of something bigger, something more graceful.”

Where else in the world does she find a little grace these days? “There,” she responded, pointing to snowy snapshots of a 1920s Adirondacks lakeside bungalow she and her husband recently purchased. Like the Algonquin, like her repertoire, like her modestly furnished, softly lit apartment, the photos radiate the charms of yesteryear. Fittingly, she had an old-fashioned knotted wood sign made to post at the edge of the property.

“Only, for some reason, they put an apostrophe before the ‘s’ in ‘The Pizzarellis,” she said, holding up the sign. “Like we’re a restaurant of something. Pizzarelli’s restaurant.” Can’t attest to the food that might be found at such a supper club. But the in-house band is something else.

Ms. Molaskey performs at the Oak Room at the Algonquin Hotel through January 29 (59 West 44th Street, 212-419-9331).