There’s something about SMILF that draws you in, even if it doesn't keep you there.

The new Showtime comedy (Sunday, 10 ET/PT, ★ ★ ½ out of four) is the latest in a run of melancholic half-hours from writer/director/actors, in the vein of Aziz Ansari’s Master of None or Donald Glover’s Atlanta. This time, the auteur is Frankie Shaw (Mr. Robot) who based the show loosely on her life.

SMILF doesn’t reach the heights of either Master of None or Atlanta but, at least in the first three episodes made available for review, Shaw has crafted a fascinating and complicated lead character, even if the series is messy in its tone and plotting.

Shaw plays Bridgette Bird, a single mother someone would like to have sex with. She's a working-class mom living in Boston’s Southie neighborhood, who cobbles together a living by tutoring for a rich white family (featuring a blissfully ignorant matriarch played by Connie Britton) and answering random ads on Craigslist while raising her son, Larry (yes, after that Larry Bird).

Bridgette has some help from Larry’s father Rafi (Miguel Gomez), but he is mostly concerned with maintaining his sobriety and his new girlfriend (Samara Weaving). She also gets occasional help from her mother Tutu, played by an aged-up Rosie O’Donnell, who has mental-health issues and a tenuous relationship with her daughter.

There aren’t a lot of laughs in SMILF. The life that Bridgette leads is hard, messy and bleak. She lives in a tiny apartment, and shares a bed with her son. She has trouble finding full-time work without reliable childcare. Her often-smiling face is a facade for a woman just barely holding on, who has not dealt with her own trauma: She talks openly about being sexually abused by her father as a child, and has an eating disorder that lingers near the surface.

SMILF often feels like a collection of scenes more than a cohesive series, and its subject matter might have been more deftly approached in a pared-down film. And, in fact, the series is expanded from an earlier short film by Shaw.

There are moments that are daring and thought-provoking, as when Bridgette answers an ad and winds up connecting with the lonely man who paid her just to show up and talk to him (before he ruins the encounter). But other scenes seem designed to shock viewers or invite them to judge Bridgette’s choices, as when she hooks up with a former schoolmate while Larry is in her bed, covered with a blanket. Shaw reaches for a misplaced punchline and the momentum of the episode withers.

Bridgette is sharply drawn, and Shaw gives the character a lived-in feel with an entrancing performance, and it's hard to look away even when the series wades too far into cringe humor. But her depth only highlights the weakness of the characters surrounding her. Britton's Ally tends to fall back on stereotypes, and Rafi is a one-note ex-boyfriend.

What SMILF does well, it does really well. There are signs of a good series, with the potential to improve.

And here's hoping it does, because we're definitely rooting for Bridgette.