HBO's new documentary about Carrie Fisher and Debbie Reynolds is the story of how two immensely talented, charming, and eccentric women needed each other.

Released over the weekend, Bright Lights follows the mother-daughter duo through Fisher's rehearsals for A Force Awakens and Reynolds' last performance and SAG Lifetime Achievement Award. It feels at times like a modern-day Grey Gardens, the famous 1975 documentary that followed another singing mother-and-daughter pair, both named Edith Beales, whose eccentricities and inordinate, even unhealthy intimacy made them compulsively watchable. There's an important difference, though: Fisher and Reynolds aren't washed up.

This is a famous pair, and Bright Lights is not about their decline and fall. Instead it's about how they narrate the complicated showbiz past that led to living together — and the closeness that would lead to them dying a day apart last month.

The documentary briskly establishes that Fisher and Reynolds' conflicts are just as chronic as their affection. Footage of Fisher as a child has Reynolds explaining — in charmingly passive-aggressive voiceover — that she took this footage to prove Fisher, who has written about being bipolar, an addict, and the product of Hollywood dysfunction, had once been happy. Fisher quibbles that of course she's been happy.

And the compound they inhabit perfectly illustrates their sometimes clashing styles: Reynolds' house is covered in comfortable, sometimes floral fabrics, while Fisher's is a Spanish-tiled mishmash of the wonderful and grotesque. As is Fisher's tour of it — she introduces the viewer to a life-sized Princess Leia sex toy and the facilities which contain, "as every bathroom should, a player piano."

In describing her home, Fisher calls it "the opposite of the house I grew up in."

The house we lived in was very grand when we were growing up. It was marble and glass. Cold. And there was just too much air in it. Family-wise, we didn't grow up with each other, we grew up around each other. You know, like trees?

The best biographies show you the gaps between the subject as they want to be seen and the subject as they are. Bright Lights succeeds on this front with Reynolds in particular. The octogenarian is the queen of smooth surfaces. After blazing through a solo act in Vegas she lurches down the steps, so spent she can barely walk. The performance doesn't drain out of her; it pops like a balloon. Legend has it Fred Astaire caught Reynolds sobbing and hiding in the middle of filming the chirpy, joyful "Good Morning" song with Gene Kelly — and that her feet were bleeding by the end of the shoot. It's fascinating to see Reynolds' iron discipline as a purveyor of effortless charm in action.

But she declines over the course of the documentary, and so does her ability to produce that charm and composure on cue. It's hard to watch mother and daughter struggle to make it possible for Reynolds to receive her SAG Lifetime Achievement Award. Fisher's efforts are heroic, her agony while her mother is onstage palpable.

And then there is their singing.

This documentary is full of amazing footage — like Carrie Fisher singing "Bridge Over Troubled Water" when she's 15 with Joplin-like ferocity. Its effectiveness is magnified by Reynolds' reaction, watching that in the present. "Love that voice," she says, choking up. "Isn't that a great voice? Wish I had it."

While Fisher refused to become a singer herself, she seems to connect to the people with whom she's closest through random snatches of song. She welcomes her childhood pal Griffin Dunne by getting him to sing a few bars of Snow White's "I'm Wishing" with her. But Fisher does most of her half-singing with her mother.

The most telling scene, to my mind, is one where Fisher walks over to Reynolds' house and observes that they're wearing the same shoes — which look like sequinned Tevas. "No, you gave me these," Reynolds says, "don't you remember?" Fisher does remember. There's no apparent disagreement here, but there's an edge to Reynolds' tone. This is not about the shoes.

Reynolds holds up a white board then and explains she likes to write messages on it, like "It's my day to be quiet and alone. Alone is good." Fisher is slumped down against the house. Reynolds bends down and says she loves her. Fisher says she loves her too, and gets back up.

"Look, we have the same shoes," she says again.

And the tension thaws. Reynolds suggests they sing a song. They noodle around lyrics and melodies, looking for a tune. Later, they'll end up warbling snatches of "I've Grown Accustomed to Her Face," from My Fair Lady. It's Henry Higgins' song about how much he misses Eliza Doolittle — who he'd found endlessly annoying, but habit has made her indispensable to him.

"I was serenely independent and content before we met," Reynolds and Fisher sing as they walk off together, arm-in-arm.

(Screenshot/Bright Lights/HBO)

If there's an element of sadness to Fisher's story — she seems to take better care of her parents than they ever took of her — Bright Lights also shows the gap between her narrative of her family and the reality. Despite what Fisher implies, Reynolds supports her daughter too. She grows teary describing the difficulties of Fisher's bipolar disease, and it's clear that Fisher depended on her mother just as much as her mother depended on her.

The burden of care is on both sides, and so, in Bright Lights, is its beauty. If Reynolds and Fisher are trees, as Fisher suggests, they're maybe closer to Baucis and Philemon, intertwined to the point where, if they didn't quite complete each other's sentences, they finished each other's songs.