It's not unusual for Tim Kinsella to choose his words carefully, but right now each syllable is being lovingly wrapped in cotton wool. The Owls frontman is talking about the making of the band's long-awaited second album, Two, which arrives thirteen years after their self-titled debut.

"A few of us are quite unique individuals," he says tentatively, when asked about the two-year writing and recording process. "We're dealing with some very eccentric people and – errr – we're very, like, thoughtful towards each other, and a way of being contemporary and a way of collaborating as best we can. Some of us are less invested in that and try to prompt others of us into the old roles. So that was tricky."

Talk to Kinsella for long enough and it's easy to see why the band left more than a decade between albums. Formed from the ashes of seminal Chicago punks Cap'n Jazz, Owls are the product of four individuals with rich and complex relationships – none more so than that between Tim and his younger brother Mike, who plays drums. Completing the picture are Victor Villarreal, whose dizzying fretwork forms the shaky foundations of each song, and Sam Zurick, whose bass parts are crucial to keeping them intact.

Despite having spent nearly two decades playing together under many different musical guises, Owls don't function like other bands. For starters, each member of the group designed one quarter of the album's artwork – in private, with no brief or any room for post-mortem. So, if you're wondering why you're staring at the bloody, disembodied head of Noel Gallagher, you have Mike Kinsella to blame.

"With most bands, you finish the record and then talk about what appropriate cover art might look like. But Owls was very much 'No no no, everyone gets their own thing. You aren't allowed to talk about what someone else does', y'know? Everyone is kind of hands-off and protective of their own thing, and I didn't know what other people had done. So Noel Gallagher is definitely Mike's comment about beating up the older brother in the band. Ummm, sooo – so I think I must be the symbolic target of it. But it's not like a comment I would have chosen to make or feel any connection to."

Tim's own collage is a distorted combination of 80s erotica, featuring underage porn star Traci Lords and Vanessa Williams, the first black Miss America who was famously stripped of her title after a series of nude lesbian photos were leaked to the press. Tim describes the process as "cutting up the forbidden porn of my youth".

Although still frequent collaborators under the revolving door policy of Tim's band Joan Of Arc, when separate the brothers Kinsella have followed very different songwriting instincts. After Cap'n Jazz imploded, the band's frantic energy splintered in almost opposite directions, connected by a loose thread of intricate guitar playing that you might recognize as the 'Kinsella sound', if such a reductive thing were to exist. Emerging behind his brother's shadow as a frontman in his own right, Mike's songs as Owen or previously with American Football are delicate, introspective things, refined over time into a tasteful and instantly identifiable oeuvre. Tim, meanwhile, has restlessly experimented with space and form, his records ranging from subversive art rock to acoustic duets and theatrical soundtracks.

Have these different experiences had any impact on Owls 2.0?

"Well, we aren't particularly impressed with each other. We all love each other, but any sort of success or anything like that doesn't phase us. We know each other too well for that. Y'know, I feel like we're better at playing together now, because we have that much more of a skill set and that much broader a toolbox to choose from and smarter choices to make – but the professional experience doesn't really [have an impact]."

It's true that Two is a very different record to Owls, its songs settling into grooves more readily without tying themselves up in knots. That isn't to say that the band has done anything quite so dramatic as change direction, but they jump between ideas less frequently and allow the transitions more room to breathe. All the flourishes are still there – from Villarreal's sophisticated leads on 'This Must Be How…' to Mike Kinsella's untraceable rhythms on 'I'll Never Be…', but they're hidden among more concrete riffs and backing beats.

"I think we wanted it to really be about the songs," explains Tim, whose solo work has often shunned traditional structures. "People often, when they talk to us about Owls, focus on the technique and the sort of technical things that aren't really very interesting to any of us. The technique has always been in service of the feeling. Even lyrically I was aware I didn't want to fall back on these 'clever' things I used to do – like, lots of wordplay and stuff. We refined these songs for a couple of years before recording, and lyrically that meant a lot of slashing away that mist of cleverness."

That much is evident from tracklist alone, which is populated by uncharacteristically plain titles that are simply swiped from the first line of each song. Compare it against those on the first Owls record, for example, which contained such meticulously constructed concepts as 'What Whorse You Wrote Id On', 'I Want The Blindingly Cute To Confide In Me' and 'For Nate's Brother Whose Name I Never Knew Or Can't Remember'.

Again, this isn't so much a flat-out rejection of old habits as it is a fine-tuning of Kinsella's writing style. The singer can still be found yelling about such abstract ideas as hornets slaughtering honeybees and masks made of dry spaghetti, but he's also singing about more literal concepts too. "I'm afraid I may have said something I didn't intend to say," he offers on the closing refrain of 'I'm Surprised', a song which appears to address the binary of nearing middle age and still living the life of a touring musician. Could it be that Tim Kinsella is opening up, after a career spent as the reluctant hero to a generation of wide-eyed emo kids?

He prefers the term 'committed' to 'open'. "I'm not going to tell people 'I feel like this' or 'you should feel like this' but it's more about putting specific objects or circumstances or words next to each other and letting something get evoked. So, in that way it's more specific in that I'm defining the constellations of objects that are being set next to each other, whereas in the past I used to use a lot of double meanings and stuff so that every phrase was slippery."

Without these barriers there are plenty of lyrical gifts to take pleasure in, with some of the most direct lines hitting hardest. For instance, "I walk away from shit I don't understand, and I don't think that's weird" is a wildly satisfying philosophy, while the hook "It's cute how you assume your experience of the world is the world" from 'Why Oh Why…" is the perfectly pointed putdown that's begging to replace 'check your privilege'.

Perhaps even more satisfying is 'Ancient Stars Seed', which is built around a hollered chorus: "We've never had nice stuff, we've never owned a nice thing / We've never really even been friends with anyone with nice stuff." Not that he'd complain about it, but after a life of playing small to medium-sized venues for a living, Kinsella, 39, admits this one feels nice to sing.

"I can't speak for all four of us, but most of us have lifestyles that aren't very common to people of our ages. Like, we all kinda live on a lot less money. Nobody would ever confuse any of us for middle class, y'know? Like sometimes I just look at the equipment that other bands have and I just think, where do you possibly get the money for that equipment? So I dunno, maybe it's just a class solidarity thing. And that said, we all have beautiful charmed lives in certain ways. It's not just like a 'we're still punk' kinda thing either, it's really that it feels good because we don't particularly find meaning in acquiring possessions. I mean, I say this as a person with a lot of books and records, but I guess it feels good because it's just a very basic calling of bullshit on consumerism."

On the subject of records, Kinsella's own discography might already be larger than the average record collection. Aside from a two year hiatus between 2001-2003, Joan Of Arc have released at least an album a year since their first in 1997 (often there have been two or three), and that's before taking into account EPs, split releases and all of Kinsella's side projects. He says he's "more invested in the process than the progress" of making records, but equally is not interested in retreading old ground.

"That's why my old records sound worse to me than any other records in the world. I've always wondered why – but then it hit me, it's because I was dealing with a set of questions or issues that I worked through in the making of the record. So now it's like – of course it's boring to me, because I know all that!

"I really feel no urgency whatsoever to ever release another record with my name on it," he reflects. "It gets harder to finish each one, because each one needs to justify itself. Like, there are enough of these already – the world doesn't need another of these records, y'know? So it does always need to make a statement that the other ones haven't in some way – just for my own investment in it."

Having said that, Kinsella admits to having demos for 40-something new songs on his computer, and will release his second novel Let Go & Go On & On next month. The two disciplines are "definitely informing each other" he says, explaining that he's wrapping his head around a few ideas that reach "beyond the carrying capacity of a pop song." Even if the next Owls album takes another thirteen years to surface, then, thankfully there should be no shortage of Tim Kinsella records to fill the gap.

Owls' Two is out now on Polyvinyl