The follow-ups that outshine the movie that came before it.

Cinemas are sweltering with sequels at the moment: Mamma Mia! Here We Go Again! The Incredibles 2! Sicario: Day Of The Soldado! Jurassic World: Fallen Kingdom! The First Purge (which is, confusingly, the fourth Purge)! Even the return of Mr Gareth Southgate has a redemptive, second-act potency. More often than not, sequels suffer from diminishing returns, but there are rare occasions where they improve on the original. Here are five of our favourites:

The Godfather Part II (1974)

The first Godfather reinvigorated American cinema with a dash of European élan, an Italian immigrant family saga with Dostoevskian moral complexities shot like a Rembrandt. It was arguably the finest English language film since WWII, and yet its sequel may be even better. People still debate to this day which is superior, but what The Godfather Part II lacks in Messrs Marlon Brando and James Caan (although the latter has an uncredited cameo), it gains with Mr Robert De Niro (a masterclass in controlled vengeance delivered mostly in a Sicilian dialect), an ambitious past-and-present narrative and the giddy mania of Mr Al Pacino’s moral descent.

Terminator 2: Judgment Day (1991)

The original Terminator (1984) was a smart, unsettling thriller that ingeniously cast Austrian weightlifter Mr Arnold Schwarzenegger as a robotic angel of death. More intriguing still (and a hand forced by Mr Schwarzenegger’s new desire for leading man roles) was to reinvent him from the villain of the first film to the anti-heroic protector of the second. Director Mr James Cameron, who’d already made excellent Alien follow-up Aliens, gives the sequel more deadpan humour, jolts of nastiness and visuals that have aged surprisingly well (the film was re-released in 3D last year). Playfully iconic zingers litter the script: “Come with me if you want to live”; “Hasta la vista, baby”; “I’ll be back”.

Before Sunset (2004)

Mr Richard Linklater’s Before trilogy follows the repercussions of a brief encounter between Mr Ethan Hawke and Ms Julie Delpy, two passengers who spontaneously hop off their train carriage to explore Vienna together. First instalment Before Sunrise, when the characters are in their twenties, was just a little too earnest, but by the sequel, this time set in Paris, the characters have grown into themselves, more endearing and with more at stake in their thirties. With shades of French master Mr Eric Rohmer, the latter is a patient, dialogue-rich, understated romance, a bookish dissection of love packed with subtext.

Logan (2017)

Of all the attempts to combat audiences’ superhero fatigue, this twist on the Wolverine story was the bravest, a noir, violent, spare psychological drama with unexpected influences. Director Mr James Mangold, who explored similar themes of aging alcoholism in his Mr Johnny Cash biopic Walk The Line, pitched Logan as a twist on Little Miss Sunshine, three generations of superheroes trapped in a van on a highway. With a textured script, emotional gravitas and offbeat cast (Mr Richard E Grant as a sinister doctor; Mr Stephen Merchant as an albino servant called Caliban), the risk paid off and the film made $619m worldwide. More of the same, please.

Paddington 2 (2017)

Sometimes the stars just align. During a year of unprecedented political turbulence, Paddington was a hero for our time: a hard-working, innocent, resourceful outsider desperate to fit in. Mr Ben Whishaw and Mr Hugh Grant, who recently reunited for the BBC’s A Very English Scandal, have a lovely chemistry. As well as its promotion of kindness and tolerance, the film mixes physical comedy, deft characterisation and an immaculate structure within which every small detail becomes relevant (such as Mr Hugh Bonneville’s coconut-throwing expertise and Ms Sally Hawkins’ swimming). A joyous, cathartic romp and the most complete achievement in animated film since Toy Story 3.

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