Among the press materials for the new Showtime comedy “SMILF” is a note from the showrunner and star, Frankie Shaw, intending to justify the title of the series—to defend against offended inquiries and preëmpt baffled commentary. The show concerns the single mother of a young toddler; the title’s root word is a familiar vulgar acronym denoting a mother’s erotic appeal. The note informs us that Shaw aims to beat the male gaze in a staring contest. “There's no real room for a woman's existence in the word MILF,” she writes. “By getting inside her life experience, we are in a sense changing the meaning, reclaiming it.”

O.K., great. More power to her. Three episodes in, I am charmed by Shaw’s way of sketching her character, Bridgette Bird, in brazen strokes of absurdity and delicate gestures of woe. But what is maybe more apt as a mission statement for the show is a brief shot of a mural overdrawn with graffiti. Defacing a basic image of the Madonna and Child, a vandal has enhanced Mary’s bosom with cartoonish arcs of spray paint. This, too, is “SMILF” ’s project: rudely overwriting the iconography of motherhood. Body comedy and sex farce lubricate the show’s engine, and healthy contempt for piety steers its way.

Off to the side of Mary and Jesus is another scrawl identifying the location as Southie, South Boston, portrayed with enough warmth that the neighborhood’s hardscrabble mood never descends into bleakness. “SMILF” has something to say about class, and it tends to say it, as it says most things, obliquely, with occasional lines devised to play to the back of the room. “You’re rich or you’re stuck,” Bridgette says in the third episode, to a john, having decided to experiment with something in the ballpark of prostitution, in order to make the rent.

Stuck is an apt descriptor of Bridgette’s own social rank. She’s definitely flat broke, but the look of her small apartment, which combines the tumult of a nursery and the sloppiness of a teen’s bedroom, and features boxes of organic cereal among the chaos, is less a depiction of indigent squalor than a sign of slapstick gracelessness under pressure. Her own mother—played by Rosie O’Donnell as an appealing caricature of an aggrieved Irish-American matriarch—handles financial paperwork ranging from lottery tickets to coupons, ritualistically scratching and clipping. But the Francophone-ish suffix of her daughter’s name communicates a certain sort of social ambition. Despite their limited means, the family endeavored to get Bridgette unstuck by sending her to a fancy prep school.

Bridgette uses this education to get a job as the tutor to a family out in Brookline or some such, where she preps the diligent daughter for an art-history exam and writes essays for the slacker sons. Her employer is played by Connie Britton, cast terrifically against type as the sort of pampered bad mother who delegates her helicoptering. She’s a yoga mom who sometimes can’t get it together to go to yoga and instead sits in her parked S.U.V. binge-eating McDonald’s. The first time you hear her tell Bridgette “You’re such a good friend,” you hear it as condescending prattle. Later, in a weak moment, she reiterates, “You’re my best friend,” and you worry that she thinks it’s the truth.

It isn’t quite clear to us yet exactly how Bridgette ended up in this spot. Perhaps it never quite will be. The three episodes I’ve seen, shaped as riffs, release biographical information and background details with an enticing, strategic stinginess. We know that Bridgette was once a professional actor, but never ascended beyond a single “Law & Order” credit. We’re aware that she’s survived some sort of sexual abuse only because she mentions it, in a moment mingling dark and light absurdities, while auditioning for a role in a public-service announcement about post-traumatic stress disorder, a gig that will pay twenty dollars and change. We know that she bore her child out of wedlock while hooking up with Rafi (Miguel Gomez), who is now an amicable co-parent, but the show is vague about the nature of their past relationship. We understand that both Bridgette and Rafi are in recovery. He’s got a year of Alcoholics Anonymous behind him, while she is struggling with bulimia, a dysfunction that “SMILF” manages to play for light comedy without taking it lightly. Then there is the matter quietly simmering in the appearance of Bridgette’s son, who, with his halo of honeyed curls, is plainly a mixed-race kid. “SMILF” has yet to explore how the issue of race in Boston affects the life of the family, but it offers that Bridgette, a high-school basketball star, has named her boy after Larry Bird, a small, dense riddle.

Through all of this, Shaw proves herself a fantastically nimble performer, by turns tough and impish. In her loopy moments, Bridgette seems to have something in common with the magnetically weird pixies played by Parker Posey, but there’s a harder set to her jaw, reflecting a survivor’s pugnacity. At one moment, inspired by Rafi’s disgustingly amiable new girlfriend, Bridgette takes a secondhand sheet of poster board back to her apartment and, while her child sleeps, prepares to assemble a collage that will aid her in imagining a bright future for the two of them. Then a cockroach rears its head on the tabletop, and Bridgette uses her incipient “vision board” to flatten it.