The sexual politics of perceived female maturity has always been a problem in this particular set of superhero films. Quite why Kara Zor-El gets to be a “supergirl” while Kal-El gets to be a “superman”, despite not being that much older, is not obvious. Even that notorious wokester Friedrich Nietzsche went with the non-gender term “Übermensch”. The issue is in fact pre-emptively raised here in an early scene, but the dialogue breaks off without the question being explicitly resolved. Maybe there is a copyright issue. If our heroine really did have a title exactly corresponding to “Superman”, the spirit of Shirley Conran would no doubt angrily barge on to the screen with a phalanx of lawyers and a bag of defiantly unstuffed mushrooms.

Well, after her brief walk-on in last year’s muddled and boring Superman reboot feature, Supergirl now gets a sprightlier and sparkier film of her own, with 26-year-old Australian actor Milly Alcock in the lead. Rising British comer Eve Ridley, as gutsy alien teen Ruthye Marye Knoll, joins forces with SG to avenge the death of her dad at the hands of the evil intergalactic human trafficker Krem of the Yellow Hills, an odious pirate who kidnaps women for breeding stock purposes, played with watchable relish by Matthias Schoenaerts. SG is after Krem, too, because he has taken her adorable dog Krypto, of all the appalling things (though sadly Krypto hasn’t yet got his own little cape). Meanwhile, Jason Momoa turns in a cheerfully cigar-smoking man-mountain performance as Lobo the bounty hunter, who is schooled by Ruthye in how to escape from prison – the movie’s one clear feminist moment.

It’s a relief to see a DC superhero film that tells a clear story, without getting bafflingly bogged down – as has the preceding Superman feature and so much of the DC Extended Universe franchise – in tangled subsidiary material and boring backstory, including the unbearably dull issue of superheroes’ relationship with the media. As for Alcock’s Supergirl, this adventure is supposed to be jolting her out of the torpid ennui in which she finds herself, always waking up late and hungover, dishevelled, sporting big goofy sunglasses like Kurt Cobain. When it comes to aerobatics, she is a big fan of rising vertically up and down, one knee slightly bent. We don’t get the classic horizontal flight mode, one fist out. Perhaps that is considered slightly lame these days. And Supergirl certainly isn’t required (yet) to model any sort of figure-hugging costume for the male gaze.

David Corenswet’s Superman has a cameo in caring big-brother mode, and a flashback to Supergirl’s own Krypton childhood and arrival on Earth (very similar to Superman’s, of course) gives us her sorrowing parents Alura In-Ze and Zor-El, played by Emily Beecham and David Krumholtz, as they take the decision to give their daughter a chance at survival. I would like to see a prequel spin-off for Krumholtz, to show us his comedy chops.

Supergirl isn’t a perfect movie by any means, but there are moments when you’ll believe this franchise can fly.