Don’t let the title fool you. Despite 20 or so bookending minutes in which photographer and artist Peter Beard reflects over old photos and some alluring footage about the innocent days when Montauk, New York, drew celebrities like Andy Warhol and Mick Jagger rather than mere kabillionaires, That Summer could more helpfully have been called More Edie and Edie or Before Grey Gardens or A Very Edie Prequel or Hey, Look What We Found! The heart of the film, about an hour of its running time, consists of new-to-us footage of those perennial documentary favorites, the reclusive Big and Little Edie Beale of the Maysles’ Grey Gardens.

In 1972, Lee Radziwill (as in former Princess Caroline Lee Radziwill née Bouvier) shlepped from Southampton, New York, to East Hampton with the idea of making a documentary about the Long Island life of her and her family, including her sister, Jackie O; why not invite their “eccentric” — that’s Radziwell’s term — Aunt Edie to participate, filming the scandalous Havisham squalor of her life, and maybe get her to sing a few songs? So, Radziwill, Beard and a film crew that included the Maysles brothers (Albert and David) entered the crumbling, overgrown, raccoon-infested mansion that would eventually become legend. The Bouvier-family documentary sputtered, and the Maysles never got access to the footage they shot in ’72; recognizing a great story when they saw one, they made Grey Gardens a year later.

Now, That Summer reveals four lost reels of Grey Gardens’ inhabitants, “Big” Edie Beale — aunt to Radziwill and Jackie O — and “Little” Edie Beale, “Big” Edie’s adult daughter. They are, here, essentially as we remember them, just a touch more self-conscious. The crucial difference: Here, the Beales are often in receiving-visitors mode, on their best behavior in the company of Radziwill and Beard. In fact, That Summer finds the dank, dark confines of Grey Gardens getting sunnier and more welcoming. Radziwill and Co. arranged for plumbers and electricians to come out and restore hot water to the property, all while making plans to dispose of rotting furniture and bags of garbage.

This footage is more incidental, less mysterious and revelatory than in Grey Gardens. But, still, it’s more of the Edies, which makes it priceless. (Goran Hugo Olsson, director of The Black Power Mixtape 1967-1975, put the film together.) Highlights include Edie the younger, again wearing black turtlenecks and marvelous headscarves, improvising a cabaret number she calls “My Adobe Hacienda.” There is, again, much ado about critters, including far too many cats: “Mother was engaged to Horace Bigelow Allen, so I named that Maltese male cat Bigelow,” Little Edie tells us. Pointing to a golden tabby, she says, “That’s Tedsy Kennedy. He has eye trouble.” Meanwhile, the raccoons eat at the roof and the scraps the Edies toss them and inspire this for-the-ages observation: “I think it was the icing on the cake that made them vomit.”

Occasionally, present-day Radziwill and Beard speak in warm terms over this footage about the intensely private lives the Edies lived in Grey Gardens. “They were in a dream world, and it was OK,” Beard says, investing OK with curious significance, as if it’s the most a person could want. But in stray moments, Little Edie seems desperate to escape: “I’ll never feel right in this place, ever,” she sighs. She often covers her face when the camera moves from her mother to her — she’s much more comfortable performing the role of Edie when alone with the crew. “If I were a drinker, I could be consuming my eight bottles of booze every day,” she confides in a stairwell. Late in the film, the Radziwill cohort departs Grey Gardens, leaving the film crew behind. Soon the Edies are picking at each other while the Maysles pan around Big Edie’s sitting room, studying the clutter. After much time spent on Big Edie’s fondness for her own portrait, Little Edie turns the conversation to the general untrustworthiness of men.

“You shouldn’t have had incest with your uncle,” Big Edie snaps.

“I didn’t have incest — I just found out about men,” Little Edie replies.

As often happens in Grey Gardens, this moment pierces through the voyeuristic skeeviness of the project. Rather than just gaping at the spectacle of Hamptons royalty gone proudly to seed, here we’re invited to ache with them, to consider whether the other options their lives offered would truly be better than their filthy yet comforting co-dependency. Not that watching this feels clean. Offhandedly, in a movie that itself is offhanded to a fault, Little Edie cuts to the core of the whole Grey Gardens phenomenon during one of her moments alone with the camera. “[To] dig up the past, I think, is about the most cruel thing anybody can do.”

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