Sinéad O'Connor's records don't necessarily reveal themselves speedily. I know that, on the first hearing, 'The Lion and the Cobra' seemed to me an ill-fitting match of various discordant styles. I didn't really crack it 'till its sixth time round my turntable.

Likewise with I Do Not Want What I Haven't Got. Again, at first encounter, it can seem an ungainly collection - encompassing Irish trad, hip-hop moves, spartan New Wave and bleakly whispered rock ballads - that initially appears as if it's only welded together by the force of Sinéad's own vocal personality.

Indeed what really can unsettle and throw the unwary listener off the track is that I Do Not Want... is neither necessarily the record she's been promoting nor the one about which the reviewers have been disagreeing. In all her interviews, Sinéad has paraded her newfound contentment and spoken of I Do Not Want... as a 'prayerful' album. And yet, though such contemplative elements exist on this record, it isn't an album to soothe the heart's cares. Rather its virtues reside in its constant sense of emotional struggle and how it keeps harking back to the painful birth-pangs of her new way of life. She may claim she now prefers to heal but, in actuality, the experience of I Do Not Want... is that of someone fighting to win her new consolations.

Indeed the misconceptions may arise from the album's only failure - ironically the title track itself - a song that's obviously intended to close and resolve the record by emphasising her new state of grace and emotional balance.

Instead, it's one of those brave shots that seemed like a good idea at the time. Sung acapella, it's meant to be her dream-state song, her mantra of a Gaelic trance-chant but, taken at an unusually unvarying tone, it won't cross the bridge of communication to all but her most zealous fans. Thus, this lone lapse entirely changes the perspective on the album. Instead of ending I Do Not Want... by thrilling to the butterfly's flight, you get thrown back to those moments where the chrysalis is being painfully escaped.

Thus you eventually uncover a record that's blunt, literal and rarely obviously allusive, one that scorns wordplay and the false charms of the pop games of the passing now. Furthermore, it's an exorcism of the many soul-bruising traumas of the past two years, a report from a casualty - but eventual survivor - of premature celebrity stress that's also an intensely personal foray into the confessional. Or to switch metaphors, it's rather like strong black coffee, with little or no saving sugar of human to soften its often sombre and sometimes harsh flavour.

It's also easy to isolate those whom I Do Not Want What I Haven't Got will not win over. This chronicle of transformation isn't necessarily going to charm many males over 25, who believe they've stabilised their emotions and their identity, a factor which may explain some of the most unreceptive reviews it has attracted.

Furthermore, I Do Not Want... isn't a record to be heard with only one ear listening. Even in its quietest moments, it's insistently appealing. Listen To Me. Those who prefer their vinyl emotions displaced and refracted into the wider world, and who flinch from the one-to-one relationship Sinéad O'Connor demands here, are likely to find it a whit egocentric, self-important even...

And yet, given the patience and empathy to get on its wavelength, I Do Not Want... is special. With The Lion And The Cobra, moments of wailing adolescent melodrama were permissible, even desirable, since they suited its scheme. But now Sinéad O'Connor's singing has entered a new plane of emotional accuracy and suppleness.

Of course, the magnificent 'Nothing Compares 2 U' will endure long past most pop hits natural radio shelf-life exactly because this song of supplication also so acutely conveys an undercurrent of sulky defiance in its confrontation of love love. I've already heard it sung by the female freemasonry on the last bus and that's the ultimate compliment.

But it isn't the only triumph. 'Three Babies' has the delicacy to walk on emotional eggshells without splintering them. And as for the arrangements on both those tracks and on the equally persuasive ballad, 'Feel So Different', the strings can even lead me to wonder if someone's been swotting up on Roy Orbison. And if not, Sinéad's certainly arrived at a similarly swimmingly moody and dramatic destination.

I Do Not Want... is monochrome, very much the product of a London exile who's immersed herself in hip-hop and tenaciously refused to let her vision be clouded by an Acid House technicolours. So 'I Am Stretched On Your Grave', her mating of Sean-nos with rap rhythms, is unceremoniously bald and unstreaked with any Celtic colour beyond a blaze of fiddle from Steve Wickham at the finishing tape. It might sound like a forced and unnatural marriage but the bleak setting entirely rids the song of any sentimental trad associations to let the lyric be nakedly reincarnate in the deathly despair of inner-city decay.

Neither healing ambient sounds not false unenduring young pop charms attract Sinéad on this self-produced record. Even the two uptempo rock tracks, 'Jump In The River' and 'The Emperor's New Clothes', keep to a narrow unswerving path, both bass-heavy and with only grainy acoustic guitars for texture.

And it's exactly this sparseness and lack of softening harmonies that give 'I Do Not Want...' its almost militant emotional purity - this is a record where every element is subordinated to her vocals. And given such uncompromising methods, anyone with even a fleeting familiarity with the Sinéad soap-opera of the past two years is bound to fasten onto the trip of songs, 'Jump In The River', 'You Cause As Much Sorrow' and 'The Last Day Of Our Acquaintance' and, yet again, be reinforced in the view that I Do Not Want... centres on the other traumatic shedding of old skins.

But it works, if one's to play the game of finding her Irish literary equivalent. Sinéad O'Connor's archetype might be Francis Stuart, a similarly stubborn, stumbling, wayward spirit who was prone to headbutt truth in his youth. And rather like him, the mortal sin she most fears is not expressing the truth of - or the intensity of - her emotions.

Which makes I Do Not Want What I Haven't Got an unflinchingly brave testament - and, conclusively, the first major Irish album of the new decade.