Here We Go Magic's third album is crucial. In the three years since the project began as a nom de plume for folk singer Luke Temple, output has been frustratingly hit and miss. Initially an attempt to strike out in directions beyond folk, the safety of the moniker was an outlet for Temple to explore. The result has been a collage of psych folk, shoegaze, dub, ambience and noise which is at once striking for its incongruence and maddening for its lack of focus.

Here We Go Magic's eponymous debut was a case of throwing as many genre-bending ideas at the wall as possible and seeing what stuck. It was rough around the edges but full of promise. 2010's Pigeons, however, was an even more sprawling proposition, with Temple and his newly enlisted cohorts (HWGM had, in the meantime, evolved into a five-piece) spurning the opportunity to sharpen their vision, instead casting their net bewilderingly wider. While the record is the sound of a band enjoying themselves, large tracts are set aside for self-indulgent, lo-fi meanders.

This time around, producer Nigel Godrich has stepped in, his apparent mission to take their still-raw potential and fashion the first truly great Here We Go Magic album. The story goes that Thom Yorke dragged a "bleary-eyed and hungover" Godrich to see the group at Glastonbury 2011 and he was sufficiently compelled to want to capture the band's unique talents himself.

Godrich admits that the end result is quite far removed from the live shows but this is no shortcoming. An altogether warmer and more restrained affair, the group have dropped novelty and sheer velocity in favour of a more mature groove on A Different Ship. Though it's always hard to measure the precise impact of a producer, it seems like Godrich – a man who famously enforced rigid deadlines when Radiohead were recording Hail To The Thief – has helped reel in the group's bent towards tacked-on instrumental excess. Gone are the cowbells, Wurlitzers and percussive haste, the producer instead finding new ways to channel their unique power. It has close antecedents in ‘Surprise' and ‘Land of Feelings' from Pigeons, but this is relatively untilled terrain for the quintet.

Eclectic as always, opener 'Hard To Be Close' is propelled gradually forward by off kilter rhythms in the vein of Vampire Weekend, while its neo-sea shanty melodies and delay-soaked guitar are reminiscent of early Coral. 'Make Up Your Mind', on the other hand, is rooted in the same blues rock soil that yielded John Martyn's 'Solid Air'. It has the feel of a seventies car-chase scene as the guitar riffs tumble and weave, while its discordant synth stabs give it a hypnotic space-age edge that's indebted to krautrock.

'Alone But Moving' is a moment of pure tenderness that stands in stark contrast to the group's previous work. Its slow, steady beat and muted guitars make room for Temple's gorgeous, introspective vocals. It's also significant in that, as the synths bristle and the choir of sampled, backwards voices swell, it becomes clear that Here We Go Magic have made a breakthrough, realising that they can build towards climax without relying on kinetic energy alone. 'Over The Ocean' takes this more measured approach even further, allowing its ever-augmenting layers to create the tension, all the while supported by an understated but precise rhythm section. The contrast makes the sonic chaos and nautical vista conjured up by Temple's lyrics all the more effective as samples float and swirl in and out of earshot, creating a marriage of sound and subject that ranks with Godrich's work on Radiohead's In Limbo.

Of course, the BPM doesn't stay low throughout. 'I Believe In Action's' battling riffs and pummeling snares could sit comfortably in the middle of a DFA sampler, while lead single 'How Do I Know' is a slice of high tempo sunshine pop adorned with hand claps and catchy, if nauseating, woo-woo backing vocals. For fans of the group's folk roots, 'Miracle of Mary' is a traditional lovesong that would fit perfectly within Temple's solo output.

Perhaps the crystallisation of the band and producer's vision comes on closer, 'A Different Ship'. Temple recently spoke of the opposing forces at work on the record, describing the music as feeling, "brittle and about to crack … always suspended in between major and minor" and as the title track's jangling chords rise and fall, they always seem to exist a beat behind or ahead of the vocals. The mood shifts from optimism to indolence in an instant, creating a dream-like and brilliantly disorientating air.

Initially Godrich wanted to faithfully capture the essence of a band who were, as he put it, "very powerful and unusual." While idiosyncrasies remain, A Different Ship is less self-consciously quirky compared with previous releases. Its twists and turns rely on timbre and texture rather than gimmick and are much more interesting as a result. Here We Go Magic have grown up on this album and the key to its success is that there is quite simply far less room afforded to self-gratification so that it moves perpetually forward, demanding attention throughout. Lacking perfection, it is a significant leap that safeguards the band's work from being classed as mere curio and shows that Here We Go Magic's star is in the ascendancy.