Cayetana. (Chris Sikich)

There’s a certain charm to the setup at the Songbyrd Cafe in Adams Morgan, where an L-shaped stage usually means the drummer is tucked almost around a corner from the rest of the band. That didn’t stop Cayetana’s Kelly Olsen on Thursday night, making her feelings known on a variety of subjects as guitarist and singer Augusta Koch dealt with a malfunctioning microphone issue. “Anyway, I’ve had a couple of beers, so . . . ,” Olsen concluded as the capacity crowd erupted in cheers and laughter and Koch’s mic was restored to working order.

The Philadelphia trio rode that spirit of spontaneous intimacy throughout an endearing, but too-short 40-minute set that perfectly suited the friendly basement vibe of Songbyrd. Kicking off a tour in support of the band’s latest album “New Kind of Normal,” Koch’s chunky guitar chords and captivating, world-weary lyrics provided plenty of shout-along moments for the audience that stretched to the room’s back wall.

While the new record slows the punk tempo that underpinned 2014’s “Nervous Like Me,” it ups the emphasis on bassist Allegra Anka’s melodic figures and drops a mother lode of lines about trying to make sense — and stay above — waves of emotional confusion and doubt. “We’re only as good as our worst moments/ Are we only as good as the worst?” Koch implored on the bounding “Easy to Love,” while the crowd rose up to sing with her on “Mesa” as she warned, “We can only hurt ourselves so long/ We can only hurt each other till it all goes wrong.”

And Cayetana pulled off the not-as-easy-as-you-think trick of counterbalancing all that emotional weight with self-effacing humor and genuine charisma. “That song makes me feel like I’m in Incubus,” Koch deadpanned after the growling “Bus Ticket,” and a between-song aside about how nervous she was before playing the set was genuinely touching.

The influence of the Philly independent punk scene and the Crutchfield sisters (Waxahatchee, Swearin’) on Cayetana’s music is clear — the trio will tour with Waxahatchee later this summer — yet their very best songs surge forward with a singular drive that suggests they could be on the verge of something spectacular. Early in the set, “Too Old for This” stayed coiled in a thicket of tom-toms and bass until lashing into a skin-tingling chorus, while the set-closing “Hot Dad Calendar” rode a delicious bass hook for three giddy minutes that felt like 30 seconds. Factor in the obvious joy the band felt at starting a tour behind a very good new record and it was easy to say Thursday night was the best kind of summer rock show. And it might have been perfect if the headliners had played just a few more songs.