Thankfully, they seem to have gone about things the right way. There's no impenetrable songs without tunes a la Nu-Clear Sounds era Ash, nor have they decided to drop any edge whatsoever and beg the American mass market to adopt them (we're looking at you Borrell and Flowers...). Sensibly, they've decided to stick to what they're best at - creating spiky, well observed little pop tunes while adding extra depth and maturity.

Alex Turner may not be in a position to write about taxi rides back to Hillsborough or nights out round Fargate and West Street anymore, but he's turned his canny eye to other matters with equal success. Reality TV stars, flirty married women, and schmoozing music promoters are all amongst Turner's targets, and he even finds the time to make some poignant observations on love and relationships.

Characters such as Brianstorm on the opening single are perfectly sketched, right down to the "t-shirt and tie combination", while the sound of Turner despairing at an X Factor world where "the kids all dream of making it, whatever that means" is an early highlight on Teddy Picker. It's all set to a huge new sound, marshalled by Klaxons producer James Ford, that's fast, frantic and unbelievably exciting in parts.

While the sound is more of an evolution from Whatever People Say I Am, there are times when the musicianship is simply thrilling. Matt Helders is on top form, drawing comparasion with the likes of Dave Grohl at times - indeed, on Brianstorm, it sounds almost as if the band have cloned him, so massive is the drum sound on the opening track. Kudos most go to Nick O'Malley too, who has replaced Andy Nicholson so effortlessly that it sounds like he's been in the band for all of his life.

It's not all 300mph guitar tunes on Favourite Worst Nightmare though - Only Ones Who Know could almost be a Richard Hawley song, with Turner crooning tenderly over some '50s guitar licks. Proposed second single Fluorescent Adolescent is possibly the catchiest thing they've ever written, a witty dissection of a relationship gone wrong with a chorus of "oh the boy's a slag, the best you ever had" destined to be sung at every festival this summer.

What is most startling though is the amount of emotional depth that Turner's injected into his songs here. Do Me A Favour, a dusty, almost Americana style number about another broken relationship is just devastating, a tale of "tears on the steering wheel dripping on the seat" while Turner "watched and waited until she was inside, forcing a smile and waving goodbye". By the ending line of "perhaps fuck off might be too kind" you're weeping along with the song's protagnisit.

There's also the dirty funk of This House Is A Circus, and the glorious rush of The Bad Thing, a hilarious tale of a cheating lover ("he's not gonna slap me, he's not the jealous type"). They leave the best to last though with the closing 505 - a poignant, yearning masterpiece which sees Turner wishing to return to his lover "waiting lying on your side with your hands between your thighs". It's the perfect closer to a very impressive second album.

Whereas the debut album felt like an old friend the minute you first played it, Favourite Worst Nightmare takes a bit of listening to. Yet the more you listen to it, the more these glorious songs reveal their delights, and soon you won't be able to live without it. The difficult second album? What's that then?

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Mercury Prize 2009 nominees