In the world of movies, the smart money is always on sequels failing to live up to the film that inspired them. Decades of cinema history offer pretty concrete evidence that the odds are always against sequels. In fact, some of the very best movies ever made have led to some of the worst sequels ever made, something we explored at length on a recent list.

Now it’s time to test the odds in the opposite direction, and to take a look look at sequels that were not only good, they were actually better than the middling to outright bad movies that preceded them. These sorts of films are rare — far rarer than bad sequels to good movies, or even than good sequels to good movies. That’s probably because bad movies don’t typically get sequels; they have to be successful enough at the box office despite their shoddiness to merit another picture. And then that picture has to do enough things differently to outperform the previous one.

As with ScreenCrush’s ranking of bad sequels to great movies, our list of good sequels to bad movies takes into account not only the quality of the sequel but also the gulf in quality between crummy original film and impressive follow-up. The list is arranged not necessarily according to which sequel is “best” — if it was, the #1 would surely be different — but by which sequel is strongest relative to the movie it followed.

Make sense? Great; let’s start talking about great sequels made from not-so-great films.

The Best Sequels Made From Bad Movies

These good movies were continuations of the stories in bad ones.

READ MORE: 20 Sequels You Forget Even Existed

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The Worst Sequels Made From the Best Movies

These terrible sequels were continuations of great movies — which in some ways made their crumminess that much worse.