It was the mid-’80s, and Freddy Krueger was having an identity crisis. The recent A Nightmare on Elm Street 2: Freddy’s Revenge had performed well in theaters, but the sequel to the smart, wickedly funny original had irked fans by slashing away narrative logic in favor of a few gruesome kills. The future of the franchise was unclear: Was Freddy just another rando big-screen stalker? Or was there still a hint of life left in the character? After Freddy’s Revenge, it was impossible to know. The film had been “a great disappointment,” Nightmare producer Rachel Talalay noted in a 2010 documentary. “There was a huge amount riding on what to do with Nightmare 3.”

When that follow-up finally arrived, it took the form of 1987’s A Nightmare on Elm Street 3: The Dream Warriors. The movie wasn’t merely an improvement on its predecessor–it remains, to this day, the most imaginative Elm Street sequel ever made. For those who don’t remember, or were too scared to watch at the time, this is the Nightmare in which a group of sleep-deprived teens, including a punk-rocker ex-junkie and a role-playing nerd, fight back against Freddy, temporarily sending him back to the grave. It’s also the one in which future Oscar-winner Patricia Arquette is nearly devoured by a giant snake-monster, not long before we learn of Freddy’s own troubled boyhood.

Dream Warriors was a goony, risky attempt to reset a franchise gone awry–as were so many other late-20th-century horror threequels: Jaws 3-D, Halloween III: Season of the Witch, The Exorcist III, Friday the 13th Part III. None are the standouts of their respective series; a few are downright lousy. But the third entry is often the most interesting installments of a long-running series, an attempt to break away from the films that came before and salvage a storyline—no matter how ridiculously.

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Such reinventions are often forged out of necessity. Throughout the ‘70s and ‘80s, horror and suspense franchises traced a predictably cash-grabby trajectory: After the first film became a breakout hit, the initial sequel served as a bloody, slightly off-centered Xerox of the original, bringing back a few surviving characters while upping the kill count. It’s a formula that made Jaws II and Halloween II such huge box-office hits. Even 1977’s incomprehensible, locust-laden Exorcist II: The Heretic–still counted among the worst horror films of all time–managed to turn a profit, thanks to the involvement of Exorcist stars Linda Blair and Max von Sydow.

By the time a third entry came along, though, audiences were ready for a change, forcing filmmakers to do whatever they could to keep the saga alive. The resulting changes could be small yet seismic: Dream Warriors worked by shedding the psychological underpinnings of Freddy’s Revenge, and simply pitting its villain against a gang of root-worthy kids. And in Friday the 13th Part III, the personality-free murderer Jason Vorhees dons a hockey mask for the first time–a decision that added an extra layer of menace to the character, and helped resurrect the series at the box office.

Most of the time, though, the third movie departs radically from the original, in good ways and bad. Instead of setting another shark tale at Amity Island, the producers of Jaws 3-D relocated the Brody clan to Orlando’s SeaWorld. The resulting movie was nowhere near as smart as Jaws, but it was the kind of dopey (and apparently cokey?) stupid-fun B-movie–giant shark attacks amusement park!–that likely wouldn’t have gotten made if not for its pedigree.

Somewhat better is The Exorcist III, which nods toward the events of the first film, but mostly plays out as a semi-decent early-’90s serial-killer thriller. And while 1985’s Day of the Dead doesn’t have a 3 in its name, the third part of George A. Romero’s zombie series does away with the frenetic pace of earlier installments, and focuses on a society that’s trying to tame the zombie apocalypse, rather than merely flee from it (it also features a terrifyingly effective dream sequence.

All of those films, even the crummy ones, were genuinely surprising, taking the franchise in new directions instead of merely repeating the blood- or pea-soup-stained antics that had come before. But no third-installment sequel was quite as novel–and as unduly punished as a result–as 1982’s Halloween III: Season of the Witch, which did away with franchise villain Michael Myers altogether. Instead, the film follows a boozy cop who tracks down a mysterious novelty company that plans to use laser-equipped, Stonehenge-powered masks to kill scores of children on Halloween night. It remains one of the lowest-grossing Halloween movies ever—yet has been reappraised in recent years, thanks to its propulsive, pulpy plot, its creeping synth score, and its unapologetically downbeat ending. The film was even referenced in the recent hit Halloween update–an acknowledgment that a sequel that was once cast out of the canon has finally found legitimacy.

There’s another reason why Halloween III is now viewed so fondly: In the peak video-store years of the ’80s and ‘90s, it was often the only Halloween movie you could find on the shelves during the spooky season. The same goes for Jaws 3-D and Exorcist III–you had to learn to appreciate their weirdness, because sometimes, they were all you had on a late-October Friday night. And now, decades later, many of the lesser-loved sequels of the time are more popular than ever. They finally got their revenge.