In 1982, two years after releasing their debut punk-northern soul statement on Searching For The Young Soul Rebels, Too-Rye-Ay shot into the world, imprinting itself with ‘Come on Eileen’, a hybrid of rock and roll, Celtic music and country-soul that took the imagination and delivered Dexys a number one hit on both sides of the Atlantic.

But it was also the cover of Van Morrison’s 1972 song ‘Jackie Wilson Said (I’m in Heaven When You Smile)’ - a song of raggle taggle beauty that was ripe for Kevin Rowland to make Dexys’ own. That, combined with his distinctive voice, as well as songs like ‘All In All’, ‘The Celtic Soul Brothers (More, Please, Thank You)’ and ‘Liars A To E’ have ensured that Too-Rye-Ay is an album with a significant legacy.

That legacy has never felt fully settled for Rowland, however, who has described the mixes as “jarring”, losing some subtleties in favour of a harder edge. Originally produced by Rowland and Clive Langer and Alan Winstanley, the record sounded almost like an old soul revue, a quality that marked it out, but Rowland felt it needed more time, asking the label for more money, but to no avail.

Since 1982 there have been a few different versions of the record. In 1996 it featured eight bonus songs, and in 2007, when a 25 year anniversary record was released, it included a 14-song live performance at the BBC. ‘Come On Eileen’ itself exists in many versions, some feature the solo fiddle playing the first line of the folk song ‘Believe Me, If All Those Endearing Young Charms’, and some begin with that inimitable bassline. Even the fact that these versions exist suggest Rowland couldn’t let it go. “The songs and performances are great, but I always felt the mixes could be better. It's my most successful album, but it doesn't sound as good as the others,” he told Retro Pop magazine.

This speaks to something more philosophical, more fundamental – is anything ever truly finished? Is a song ever really finite? Having had forty years to muse on it, surely Too-Rye-Ay As It Should Have Sounded is the definitive statement of Rowland’s and Dexys’ original vision?

This impulse to revisit has always existed across many disciplines, but song is such a flexible form that it can breathe and shapeshift unlike many others. It is there in the different versions of, for example, folk songs, and it is there in an album like Kate Bush’s Director’s Cut in 2011, where she remixed and sometimes re-recorded songs from earlier albums The Sensual World and The Red Shoes. For Bush, it was about returning to an original idea that was in some way thwarted first time around, and for Rowland, there seems to be the same impulse, not only to execute his original vision, but return it to the audience.

This record contains very specific shifts - On ‘Liars A To E’, backing vocals are brought down an octave; on ‘Plan B’, the brass comes in earlier, and the female speaking role is replaced by Rowland. ‘Until I Believe In My Soul’ loses the penny whistle in favour of “Big” Jim Paterson’s trombone, which serves to remind that the original recording wasn’t without its difficulties, with Paterson (then Dexys’ co-leader and co-composer) leaving around that time in order to create an independent horn band. But with Rowland’s persuasion, he stayed long enough to record the album and perform it in concert.

Revisiting and refining can also be an emotional pursuit, because you may also be revisiting and refining memories. That emotional punch is present here too, and with the clean-up of various pops and noises (thanks to technological advances) it allows that aspect to come to the fore. A major difference is that a remixed radio edit of ‘Old’ will be released as a single (which it wasn’t originally) and there are some previously unreleased outtakes, B-sides, and a full rendering of the 1982 Shaftesbury Theatre concert.

However, the focus here is on the studio record of Too-Rye-Ay, and this version enlivens the fact that this is also a great pop album, an unconventional, trailblazing, wonky piece of art. It created a universe where a tattered, sensual ballad like ‘Old’ can sit easily with the triumphant ‘Let’s Make This Precious’ – full of glorious horn section, strings, incredible organ, and a soulful vocal performance by Rowland that teeters on the explosive – itself an exciting distillation of the Dexys spirit, replete with handclaps.

A project like this can resemble a conjuring of a central spirit, and a kind of rejoindering. And while it is fair to say that Rowland and Dexys can never be accused of being complacent, they have always been “searching for something” (to borrow from ‘Plan B’).

“Big” Jim Paterson has previously talked of Dexys line-ups never lasting more than a year, because Rowland was always thinking where to take things next. Equally, however, it is because Rowland embodies Dexys, and not just the Dexys “sound”, but in how that sound can be applied elsewhere. On 2016’s Let The Record Show: Dexys Do Irish And Country Soul – we were taken on a root through songs as diverse as Seán Ó Riada’s ‘Women of Ireland’, Diane Warren’s ‘How Do I Live’, Johnny Cash’s ‘Forty Shades Of Green’, and Joni Mitchell’s ‘Both Sides Now’ – it resembled a dialogue of sorts, a conversation worth listening to.

But back to legacy again - this project is a timely reminder of Kevin Rowland’s and Dexys impact and importance. Too-Rye-Ay As It Should Have Sounded is an exercise in clear-eyed obsessive brilliance; the free-jazz elements somehow seem even more amplified on ‘Until I Believe In My Soul’, and it now seems so striking how influential something like ‘I’ll Show You’ must have been on Mike Skinner, who surely borrowed elements of Rowland’s nonchalant spoken word (“if you see a man crying, hold his hand, he’s my friend”). It all adds up to a pure kind of poetry that was so compelling in 1982, but even more engaging forty years on.