The big surprise of the new action-comedy Spy is how much of an action-comedy it actually is, as opposed to a comedy that's got some dog-ends of action in it. For a film directed by Paul Feig and starring Melissa McCarthy - a partnership that has resulted in Bridesmaids and the much more overtly comic action-comedy The Heat - the amount of time that the film spends straightforwardly aping the James Bond formula rather than parodying it is honestly kind of baffling, though the results aren't necessarily better or worse for it. But it's not as funny as they say it is, simply because it doesn't have as many jokes as it would need in order to be that funny.

Even so, it's by far the best showcase McCarthy has had in any feature film to date, and it was clearly designed as such by her admiring director (Feig wrote Spy in addition to directing it, his first credited feature screenplay). She plays Susan Cooper, a CIA agent who, for reasons of limited self-confidence in addition to being played by the men in the agency, has never gone into the field, but spends her time whispering into the ear of Bradley Fine (Jude Law), a full-on Bondian superspy, and using all the highest of tech to guide him through his missions. As happens in movies of this sort, one particular international villain, Rayna Boyanov (Rose Byrne), the daughter of an arms dealer accidentally killed by Fine in the opening sequence, has acquired the names and faces of all of the CIA's top agents, and to take her down, director Elaine Crocker (Allison Janney) needs to send somebody with no field experience at all, somebody so plain and blandly middle-American that they can pass unnoticed. Someone like Cooper, as you already knew, or there wouldn't be any movie. This gesture raises eyebrows, the most angry pair belonging to Rick Ford (Jason Statham), who furiously quits the agency to hunt Boyanov on his own; meanwhile, Cooper is stuck into a variety of humiliating "fat cat lady" disguises by Crocker in order to pass as a boorish American tourist and thus invisibly draw close to Boyanov, aided by her best friend Nancy Artingstall (Miranda Hart) as her own handler.

None of this is presented ironically, understand, which makes this film, after The Heat, the second consecutive Feig/McCarthy joint to celebrate the talents of people keeping law and order (violent cops, the CIA) who are maybe not the best candidates for unironic celebration in the 2010s. Which can't help but hurt the film's comic elements, for me at least. That, coupled with how much of Cooper's spy career is presented without any kind of goofing around or mockery, and it proves to be the case that McCarthy herself doesn't get to do much comic heavy lifting - she's the straight woman in her own vehicle. She is, to her credit, genuinely good in the role of Cooper and her various put-on identities, an average person dropped into a crazy situation who's immensely likable and sympathetic, in no small part because McCarthy has such an affable screen presence when she's not compelled to wallow in the "vulgar and awful" trenches of the unwatchable Identity Thief or last summer's shrill, flop-sweaty Tammy. And also because she's so good at puncturing the self-importance of the characters surrounding her with well-timed tart sarcasm; her best comic gift is impeccable timing, and as the central character in a plot handled to her by a director who wants to make her look as good as possible, she's never demonstrated that timing better than in Spy.

Still, even if it's her movie, it's not a movie she can hold on to: it is stolen, and not with much visible effort, by the knockout combination of Statham and Byrne, who between them get all of the best laughs and most exciting line readings. Byrne especially. Statham is delightful and all, playing his long-established persona as a growling tough guy as an absurd comic figure so growly that even when he's making an ass of himself, he doesn't yield a fraction of an inch of granite self-assurance (he's had fun with himself like this before - the Crank movies, if nothing else - but not to such pure comic effect). But Byrne is really, truly special. She adopts an accent that's not quite her character's native Bulgarian, but more of a generalised "haughty Eurotrash" tone, and she locks herself into a steely personality of absolute arrogance and disdain, and she can make even the most unassuming lines land with the full force of an overwhelming personality. It's as tightly-wound as any performance in recent memory, almost more anti-funny than funny, and Byrne is absolutely the best thing Spy has going for it.

Because, in truth, the movie's got plenty of room to be better. It is, ultimately, a Paul Feig picture, and like both of the ones preceding it, there comes a point, or many of points, where one desperately wants him to find an editor who'll give him a hard time and demand that he makes harder choices - Spy was cut by Mellissa Bretherton and Brent White, who both worked on The Heat, and both came up, like Feig himself, through the Judd Apatow school of film comedy, where the important thing is to let improv flow freely, to encourage the actors to hang out in scenes and enjoy stretching out moments, and then, and this is the important part, not trimming any of that fat away when you're done. This mentality hasn't yet resulted in a truly great film that's free from meandering bloat or dead-end indulgences, and given that Spy wants at least as badly to be an action thriller as a comic jaunt, it's particularly noticeable how many scenes (especially the ones involving Statham) drag on, and how weirdly the plot moves and then stops and then races, and then stops again.

But even without being a comic masterpiece, Spy is undeniably a good time, with McCarthy being an utterly pleasant presence to hang out with and most of the team surrounding her providing enough personality and spark to keep things undemandingly silly (the weak links are Law, tripping over an American accent, and Bobby Cannavale, with a terrible under-written part as the other villain). It's from the "breezy lark" school of summer movies, and it's a perfectly satisfying example of that form. Better than that fatty falling down and going boom, any day of the week.