Parquet Courts is half a good punk band and half a somewhat dull psychedelic one — at least sonically. But that juxtaposition, on display during their 3 p.m. ACL set at the Barton Springs stage on Sunday, is extremely intentional, making the Brooklyn band quite interesting, especially considering the content of their lyrics.

Parquet Courts broke out in the indie scene in 2012 with a meandering, obscenely catchy low-fi song called “Stoned and Starving,” about being stoned and starving (in the “damn I want some Swedish fish” sense, not the “I am experiencing food insecurity and am a victim of systemic injustice” sense.) But over the course of their career, they’ve transitioned to commentary about subjects such as the latter form of starvation, poverty, political apathy, American violence, and the power of collectivism. It’s important stuff, and their lyrics tackle the themes in a very intellectual way.

“Those who find discomfort in your goals of liberation will be issued no apology,” are the final words of “Total Football,” which during their ACL set they followed with a particularly explicit sentiment about Texas Sen. Ted Cruz.

Every Parquet Courts’ set — and this was no exception — proves that the band consists of absolutely excellent musicians. They’re dynamos, able to control their instruments to such a degree that they can practically talk with them. And what they do — interspersing long, slow, intricate jams with crashing speedy bursts of punk — is conceptually very playful, and I love that.

In a live setting, it’s jarring, again very much on purpose. Instrumentally, it can be an extremely exciting experience, having things shift from post-rock to funk to punk to psychedelic to hard 'n' and roll to noodling to a cowbell. The crowd, certainly, was bobbing and jiving for almost the whole hour.

But, it’s also somewhat hard to hear the lyrics, which is a big deal when there’s so much effort put into the meaning behind them, and the sonic elements of many of the songs don’t necessarily convey a strong sense of urgency or protest. It’s challenging to tell that they are a political band except when the members are telling the audience, extremely sincerely but in a self-aware monotone, to be sure to vote.

Parquet Courts jam ... a lot. They delivered a good 10 minutes of instrumentalism toward the back half of their ACL set. But the highlight for me was the one-two punch of two early songs, “Master of My Craft” and “Borrowed Time,” which are personal and not particularly political but have a riotous punk feel that monumentally brings up the energy of any live show.

The band’s stage presence is sort of choreographed apathy, like they take themselves extremely seriously while also firmly believing that they and much of everything around them are a bit of a joke. I’m quite fond of that about them, too, although it’s hard to register what’s earnest and what’s jaded and ironic. At the end of the day, though, I think they’re having fun, which is nice to see.