The musical act “Speedy Ortiz”.

The Northampton-rooted band Speedy Ortiz has made four albums, but you’ll only ever hear three of them.

Beginning in 2014, the indie quartet spent two years working on its in­tended third album. Then the 2016 elections rolled around, and frontwoman Sadie Dupuis realized the songs she had weren’t saying enough.

“I wanted to be truthful in talking about my feelings about the world, and it didn’t seem right to put out an album that didn’t reflect that,” she said this week. She had said in a press release that the abandoned songs were “strictly personal or lovey-dovey” but clarified that this week.

“They were just personal or emotional in a different way. They didn’t talk enough about the people who live in this country that don’t value other people’s emotions.”

That doesn’t mean that Dupuis writes a lot of obvious protest songs. Also a poet whose first book, “Mouthguard,” was published this month, she wraps angular lyrics into haunting pop tunes. The finished album, “Twerp Verse,” includes a few deceptively pretty songs that look at the toll that the modern political era can take on the psyche. The darkest and most direct one — “Villain,” about sexual assault — was held over from the original sessions and became the new disc’s third single.

“That’s a subject that will continue to have relevance, and it didn’t seem like a thing to be implicit about,” she said. “In gen­eral, I like writing lyrics that are more like riddles and take a few listens for you to get your own meaning from. Whether I’m writing about politics or something else, I try not to go for the easy line.”

The most pop-friendly of Speedy Ortiz’s albums, the new disc harks back to the heyday of such thoughtful Boston bands as Throwing Muses, Helium and Come.

“I’ll add the Swirlies to that list as well,” Dupuis said. “Even before I lived in Boston, a lot of those bands were heroes to me. I’m a huge fan of anything Mary Timony does, and I’m lucky to have become friends with her. … There are people who think of us as a ’90s-aping grunge band and got nervous when we started using synthesizers. But I did a solo project before this album where I was looking at contemporary pop, and our drummer was listening to a lot of Prince. So it seemed natural to bring some of that into Speedy.”

Another side of the band is their love for comic art; the name Speedy Ortiz comes from a character in the “Love & Rockets” comic. And some big names in the comic world are also fans of the band. Earlier this year, they were added into an Archie comic book, judging a battle of the bands that included the Archies and Josie & the Pussycats.

“I grew up reading those comics. My mom would buy me issues when I was a kid,” she said. “As someone who grew up dressing up as (‘Archie’ character) Veronica Lodge for Halloween, it was kind of a dream for me.”

Speedy Ortiz, at the Sinclair, 52 Church St., Cambridge, Tuesday. Tickets: $15;