French Connection II: What's the best sequel ever, and why?

I watched French Connection II this week, not bad as sequels go, but kilometres short of the original. I don't remember The French Connection having to fall back on clichés the way the sequel did, for one thing (The disaster-movie scene at the dry dock, Hackman rescuing his French colleague/adversary, the "but now it's personal" ending, and one or two more).

One nice touch: Bernard Fresson's Henri, as the colleague/adversary, physically resembles Eddie Egan's Simonson, the supervisor with whom Hackman clashes in the first movie. That's a much subtler tribute to the original than is the window-glancing in the foot portion of the sequel's climactic chase scene.

Now, here are your questions: 1) What are the best crime-movie sequels ever? (Extra points if you don't mention the obvious Godfather, Part II), and 2) What are the ingredients of a good sequel?
© Peter Rozovsky 2015