The Girl With The Dragon Tattoo, David Fincher, 156 mins (18) **Mission: Impossible - Ghost Protocol, 133 mins, Brad Bird (12A) ***

Hiring David Fincher to direct the American remake of The Girl with The Dragon Tattoo, the first part of Stieg Larsson's Millennium trilogy, must have seemed a smart move by the producers. The gothic matter of family secrets, ritual murders, dogged sleuthing and state corruption looks an ideal fit for a film-maker who's delved deep into the psycho-horrors of Se7en and Zodiac. Yet while you can depend on Fincher's immaculate visual style as much as on his nose for moral putrefaction, it's hard to see how he has enhanced the Swedish original, or even much changed it – aside from getting rid of the subtitles that US audiences find so tricky.

It begins, topically enough, with a journalist in disgrace. Mikael Blomkvist (Daniel Craig) has come off worse in a libel suit against a corporate bigwig, a loss which has bankrupted him and may put his campaigning magazine Millennium out of business.

In order to claw back some self-respect (and cash) Blomkvist accepts an invitation from a wealthy retired industrialist, Henrik Vanger (Christopher Plummer) to re-open a cold case: the disappearance and probable murder of his beloved niece Harriet back in 1966. This entails a trip to the Vanger estate in north Sweden, where the temperature is as chilly as the relations between the various Vangers, a mix of reclusive old Nazis and frightful termagants who don't want a journo rummaging in the family history.

Meanwhile, Blomkvist gets his own research hireling in the extraordinary form of Lisbeth Salander, a computer whizz with zero social skills but an incandescent sense of purpose. As played by Rooney Mara, she's a slight, whey-faced child-woman with piercings, tattoos and a spiked black haircut of terrifying unattractiveness. Think of a cross between Marilyn Manson and Maria Falconetti's martyr saint in Dreyer's The Passion of Joan of Arc, and you're almost there. Lisbeth is a ward of the Swedish state and thus vulnerable to a guardian who inflicts sexual humiliation on her, and later a gruesome rape, in return for the allowance that's her due. He will be made to regret his crimes in a revenge that suggests her own brutalised education in porno-violence.

Larsson fans probably won't mind, but this latest Dragon Tattoo fails to justify itself so quickly after the Swedish version. The photography is crisper, the grooming is slicker, the production values are ritzier – and it has Daniel Craig, lightly Scando-accenting his English in the first scenes before dropping the pretence. Fincher, working from a script by Steve Zaillian, ticks off all the plot points and makes good use of some lonely snowbound locations.

Yet it feels like a real footslog, and the running time suffers from serious bloat: Craig moodily scrutinising his board of notes and photographs or Mara swapping glares with an archive librarian leave no doubt as to their diligent clue-hunting, but as a mystery it's strictly uninvolving. Even at the ghoulish climax, when a character is trussed up in a sicko torture-basement, the mood is punctured by the villain's choice of soundtrack – Enya, for crying out loud (or was that part of the torture?). Either way, this is solemn, plodding stuff that promises little for its second and third instalments.

I had a much better time, surprisingly, at Mission: Impossible – Ghost Protocol, the fourth outing for Ethan Hunt and his brand of improbable derring-do. Tom Cruise, lynchpin and producer of the series, has enlisted Brad Bird as director on the strength of his Pixar/ Disney digi-mation wonder The Incredibles. It certainly pays off in the quality of the stunts, though in terms of characterisation it falls somewhat short of the latter's Mr Incredible, Elastigirl and Edna Mode. No matter, this is high-octane entertainment, and a chance for Cruise to show himself as a team-player instead of a preening one-man band (see, don't, Knight and Day etc).

It falls into three distinct phases, the first in Moscow where Hunt (Cruise) is sprung from prison courtesy of his techie sidekick (Simon Pegg) only to land in diplomatic doo-doo after the Kremlin is bombed. It's actually the work of nihilist nutter Kurt Hendricks (Michael Myqvist) who wants to destroy the world – don't they all? – and is this close to getting his hands on Russia's nuclear launch codes.

But Hunt's Impossible Mission Force, which includes Paula Patton and Jeremy Renner, cop the blame for the blast and are hung out to dry by the US government. Can the rogue crew, stripped of back-up, foil Hendricks's plan?

The cool thing about this lot is that they don't need the government or anything else – they've got back-up coming out of their ears. Take that invisibility-shield gadget, for instance, or those computerised contact lenses, or the climbing gloves that stick like flypaper to hard surfaces. These last prove useful during the film's thrilling middle section in Dubai, when Hunt has to climb the sheer face of a vertiginous glass-walled hotel (it's the Burj Khalifa, currently the tallest building in the world). This sequence, shot with Imax cameras, lends a vaulting sense of space that might just cause your stomach to lurch. Hats off to Cruise, currently the shortest leading man in the world, who did his own stunts. Back on terra firma, the subsequent chase through the city, now immersed in a sandstorm, rounds off the most satisfying passage in any M:I movie.

It's riven with absurdities, of course, both large and small: the leather blouson that Hunt wears for a disguise is nicked from a washing-line. What's a leather jacket doing on a washing-line? But Brad Bird whips it along with such verve, and at such a pace, that – daft as it is – the thing works.