Memory always gets the last cut in editing any beloved classic film we embraced, way back when.

I recall the totality of writer-director Jim Jarmusch’s work in his indie make-or-break years, the 1980s — the impromptu road trip to Florida of “Stranger Than Paradise,” the Memphis hotel clerk (Screamin’ Jay Hawkins) and rockabilly Japanese tourist couple obsessed with Elvis (her) and “Carrull Perkins” (him) of “Mystery Train.”

But I’d forgotten the whole “how they wound up in prison” prelude to “Down by Law,” a 1986 movie and music nerd’s take on prison escape stories. It has New Orleans at its pre-Katrina seediest and features Jarmusch at his “indie artiste” peak — filming in black and white, confining the most potent action to “off camera” so as not to break his “some people will find this boring” spell, casting for hipster street cred more than anything else.

That prelude has picturesque, down market street scenes, Edward Hopper compositions in the night shots, litter and decay and pimps and hints of domestic violence egged-on by women and the good fortune of landing Ellen Barkin for those early moments, already in “The Big Easy” to film her big budget thriller breakout role.

Jarmusch needed her as a fiesty girlfriend who kicks D.J. Zack (Tom Waits) to the curb — literally — in a prologue that shows a couple of characters, a pimp (John Lurie) and that fired-and-fired-again D.J. Lee Baby Sims (Waits) get “set up” and busted for child prostition and a body in the trunk of a Jaguar a sketchy guy just wants driven “across town.”

Fire-breathing Barkin and the screwy Italian tourist (Roberto Benigni in his American cinema debut), taking notes on Southern American idiomatic English, are the life of the film’s opening act, which has only one character (played by Rockets Redglare) attempt a New Orleans drawl and the “set-ups” so obvious that their victims complain about their obviousness.

It also makes us question early Jarmusch favorite Lurie’s presence in the cast. It’s a good thing he’s been an exemplar of cool and artistic versatility (a funky jazz saxman and painter). Because Lurie’s physically in the early scenes, but his shrinking presence and unemphatic, whispered dialogue creates a vacuum where a hustling pimp is supposed to be. A veteran of Jarmusch’s “Stranger Than Paradise,” he’s just bad in the early scenes, only coming into his own after everybody’s locked up together in The Joint — the Parish prison.

But once they’re behind bars — with Zack and Jack staring each other down because neither one is all that tough — in a tiny, quiet cell where a guy can’t even get a light for his smokes when he wants one, “Down by Law” finds its tone and its voice. And only when Benigni’s Roberto, aka “Bob,” gets tossed in there with them does the picture’s comedy take off.

“Eef looks can keel,” Bob declares, in his best imitation American movie dialogue, “I yam dead man!”

Bob’s a peace keeper, coming between the two “tough guys,” keeping the focus on those who imprison them. If it takes starting a chant-a-long that ripples through the entire cellblock, threatening to erupt in a riot, to distract Jack from Zack and vice versa, Bob’s your man.

“Aye scream YOU scream, we ALL scream for ice-a cream!”

Bob’s noticed something about “the yard,” a way out. Next thing we know the Parish Prison trio are dashing and splashing across the bayou, feuding, splitting up and reconnecting all along the way to “Mississippi,” “the closest border” Jack insists. No, “TEXAS,” Bob pleads.

“Strange country” he says of the state to the west. “I see MANY films!”

Jarmusch polished and perfected his “deadpan” phase through “Mystery Train” (1989) and the seminal, all-star international taxi drivers around the world spectacle “Night on Earth” of 1991.

But Benigni was a harbinger of less deadpan movies to come. He chatters away and sweetly takes over “Down by Law.” And as a Roman taxi driver who wears his sunglasses at night and scares a poor padre to death with his unfiltered, depraved, driving and breathlessly blurted confession, his reputation in the U.S. was made and Oscar glory a mere matter of time.

Jarmusch’s most notorious years — pre “Broken Flowers,” his 2005 national “comeback”/”coming out” — were fun, because not everybody was a fan. Seeing his films at one of the last single-screen Manhattan movie houses (the Paris), at the New York Film Festival or at the Beverly in Los Angeles, as I did, was like “Rocky Horror Night.” You were in a room filled with like-minded fans, eagerly anticipating the next hip happening he served up.

“Down by Law” isn’t the Jarmusch film listed with the National Film Registry for perservation (“Stranger than Paradise”). And for my money, his best and most fun films were the ones that came right after this — “Mystery Train” and “Night on Earth.” “Coffee & Cigarettes” had its moments, and “Broken Blossoms” was uncharacteristically sweet for him and for star Bill Murray.

But look at the way Lurie and Waits dress in “Down by Law” before and after their prison clothes. Decades of future hipster shirts, hats, pants, suspenders and facial hair was laid out for us and we didn’t even know it.

Drink up the dry opening act, with its predictable “set-ups,” and wait for our filmmaker to pack three guys — two of them music legends — in a cell and then on the lam together. Relish the Waits songs and Lurie score.

And watch these two influencial fringe figures from music who also happened to ac take a back seat to the Italian dynamo the minute Benigni shows up. Sure, he’d wear out his welcome in America sometime after “Life is Sweet,” when “Son of the Pink Panther” should have finished him. But here, he’s just the latest “discovery” of a filmmaker who more than most represented New York indie cinema just as it hit its peak.

Rating: R, sexual situations, physical violence, profanity

Cast: John Lurie, Tom Waits, Roberto Benigni, Billie Neal, Vernel Bagneris, Rockets Redglare and Ellen Barkin

Credits: Directed by Jim Jarmusch An Island Pictures/Janus Films/Criterion release on Tubi, other streamers.

Running time: 1:47