The quartet's breakthrough second album, Light Up Gold, won huge praise when it was released in 2012, and saw comparisons made to an endless array of rock bands, from the Velvet Underground to Sonic Youth and Pavement.
Now bassist Sean Yeaton hopes that the follow-up, Sunbathing Animal, will place the focus on the present, rather than nostalgia.
"I don't understand the instinct people have to use the past to contextualise the present," he says, speaking ahead of a gig at SWG3 this Saturday.
"It's easy to say this band is a mix of all these other bands and if people think we're Pavement meet the Velvet Underground then fine - I'm not going to do a Mark E. Smith and say that I hate that, but I'd prefer journalists to use it in a more contemporary way.
"Every band has a narrative that's pushed on them comparing them to the 90s or the 70s, and what does that say about now?
"It can be flattering but we're at a point where it seems fair to me for us to be our own band."
Sunbathing Animal should certainly do that.
It takes the energy and punkish swagger of the band's previous work and takes it in new, still noisy directions, like the six-minute long She's Rolling.
While Light Up Gold was rattled through in just three days, Sunbathing Animal was created over three separate batches of recording sessions, while several of the tunes had been written and performed live before the group even hit the studio.
"A lot of these songs were written having spent a lot of together on the road, and then came together in a live setting, which goes back to how we made the first record," adds Sean, referring to 2011's American Specialties record.
"We learned a lot about each other as we played. It's a lot different to Gold but who would want the same record all over again?"
Although three of the band originally hail from Texas, Parquet Courts are now based in Brooklyn, where they've been since forming in 2010.
They've got three albums and an EP under their belts already, which is part of the reason that Sean is fed up with the group being dubbed as slacker-rock, due to alleged similarities with Pavement, the often shambolic California indie-rock band.
"I definitely don't agree with it," says Sean. "We tour relentlessly, we release a lot of records pretty quickly and as a band we're together a lot.
"We put our heart and soul into this, and it's annoying to read the slacker thing, although I don't think anyone means anything bad by it."
A happier prospect is their British tour kicking off on Saturday at SWG3, even if when Sean answers the phone for this interview he's fresh from trying to sort out a passport problem that could affect upcoming dates in Japan.
The prospect of playing in Scotland is a lot more straightforward in comparison.
"We've only played once before, on Halloween last year, and it was awesome, we had a really great time," he says.
"We are gigging the next day but I'm assuming we'll have some time to hang out and I'd love to go out and get some food and have a good time after the gig.
"I might be exhausted, but I want to try one of those deep-fried pizzas when I'm there…"
He might be considering damaging his arteries, but the band's overall health is looking good.
Sean reckons one advantage they have is that each member has an equal say in how things are run.
"We're very democratic as a band," he says.
"We've not just got one songwriter who's like a president saying 'This is how things need to sound'. We trust each other, play off each other and the ideas are fleshed out together.
"We're a rock'n'roll band in what I believe is the truest definition of the term."
And he believes Sunbathing Animal displays that.
"This record's a document of four people living together and playing hundreds of shows, and all that sentiment was then trapped under a glass," he adds.
"It's four people who love playing music, just playing music."
l Parquet Courts, SWG3, Saturday, £12.50, 7pm