Prising themselves free from their mid-90s fixations with irony and Las Vegas glitz, U2 have circled back to what they've always done best. That means big tunes, thumping beats and soaring guitars, while Bono pins his heart on his sleeve and sings as if he fears it might be for the last time. This is U2's most accessible and emotional recording since 1991's Achtung Baby. Not that there are many similarities between the two. Where Achtung reeked of trauma and decay, All That You Can't Leave Behind reaches out to a wider world and a brighter future. Where the Achtung songs loomed out of a poisonous industrial murk, the new ones keep the instrumentation simple and the colours refreshingly bright.

Tucked among the production credits, behind hoary old regulars Daniel Lanois and Brian Eno, is a startling name: Richard Stannard, erstwhile sonic navigator for East 17 and the Spice Girls. It seems that U2 wanted their message to come over loud and clear, and they're inviting you to join in. From the opening strains of Beautiful Day, this is a disc crammed with songs you can sing in the bath, in a car or, of course, in a football stadium, their ultimate and ill-deserved fate.

It's amusing to recall a remark Bono made during the band's earliest days, when he explained the U2 played exclusively their own compositions because they were too incompetent to play cover versions. Over the years, despite their sometimes oppressive big-rock reputation, they've developed into a bona fide hit factory, and there's an abundance of potential 45s here. Beautiful Day, the first to be released and last week's chart-topper, strikes an appropriate note of putting the past behind you and getting on with the rest of your life ('What you don't have you don't need it now'); it's abetted by a bustling beat, a contagious chorus and vintage guitar chimes from Edge.

Stuck in a Moment You Can't Get Out Of is a vast, soulful ballad with all the trimmings (gospel choir, piano, horns, imaginary lighters waving aloft), sung in Bono's finest pulpit-bashing vein. In Walk On, the band lock into a punchy medium tempo while the extrovert vocalist exhorts persons unknown to straighten up and fly right: 'Walk on, walk on, What you've got they can't deny it'. Behind him, an industrial-sized head of steam stokes up and Edge's guitars howl like the backdraft from a low-flying 747. To demonstrate that the mature rock'n'roller can still shake a leg and blow out a few speakers, they've spliced together an irresistible mix of crude techno and raw guitar-swagger in Elevation, the closest to leathers-and-grunge that U2 have come in many a year.

Indeed, after their period of epic bombast, U2 have grasped the value of simplicity. It's easy to imagine the overblown mess they might once have made of Peace on Earth, but here they use its acid lyric about death and suffering (could be Ireland, could be Gaza, could be anywhere) in scathing counterpoint to the tune's Christmas-jingle feel. The truth about less being more is also illustrated with exemplary finesse on In a Little While. Over a simple guitar figure shoved forward in the mix, Bono rasps a confessional lyric about love battered and broken but, he hopes, about to be mended if he can make himself grovel sufficiently. With a couple of smart twists, they convert this into a classic pop moment, while Bono's hoarse and desperate vocal carries the song's meaning more vividly than his words. He brings to the repeating refrain, 'slow down my beating heart', a luminous inner glow.

As the disc winds to a conclusion, it becomes more minimal and less overt. New York is an intriguingly bleak little tale about displacement both geographical and emotional, which wouldn't have sounded out of place on The Unforgettable Fire back in 1984. Grace is a weightless meditation with vaguely Buddhist overtones ('Grace makes beauty out of ugly things') and would have made a far more satisfying conclusion than The Ground Beneath Her Feet (lyric: Salman Rushdie), which has been tacked on exclusively for the album's UK release. More, remember, can be less.