Neko Case, k.d. lang and Laura Veirs wrote the songs on “case/lang/veirs” together. (Jason Quigley)

Three years ago, alt-rocker Neko Case got an email out of the blue from country-pop star k.d. lang. Also cc’d: indie-folkie Laura Veirs. Subject: “New supergroup?” OK, maybe that wasn’t the actual subject line, but lang was proposing that the three record an album together.

Case and Veirs said yes right away, and case/lang/veirs was born.

“At first we wanted to make kind of a punk-rock girl record from the ’60s,” Case says. “But the songs … were making their own sound.”

The resulting album, June’s “case/lang/veirs,” includes 14 original songs, some with lush harmonies (“Atomic Number”) and others that showcase the singers’ distinct voices and styles (Case’s enchanting “Delirium”). Express spoke with Case ahead of the new trio’s two nights at the Lincoln Theatre next week.

Is case/lang/veirs a collaboration or a group with its own identity?
We’re very different singers and songwriters, so we do poke out here and there, but I think we did achieve what we wanted, which was to write the songs and make them a cohesive unit. It’s something people [collaborating] don’t do very often — actually write each song from the ground up together. We wanted it to be like we were a band.

Where do you see case/lang/veirs going in the future?
We’re definitely having a really good time touring, so hopefully we’ll do more touring. As far as another record, I don’t think we’re opposed to it, but we each have a solo record to make first.

Live, you’re covering Patti Smith’s protest song “People Have the Power.” How did you choose it?
That was my idea; I’ve always just loved that song, because it’s so powerful and so inclusive, and it’s really fun to sing. … That song has always kind of made me cry every time I hear it. It’s a f—ing great song.

In “I Want to Be Here,” you sing: “The hungry fools/ Who rule the world can’t catch us/ Surely they can’t ruin everything.” Is that a political message?
That song wasn’t political about a certain time or place, but it has become eerily relevant lately, and it’s actually been freaking us all out. … It’s one of the songs that we do three-part harmony on, [which is] really so fun. It’s just like gliding in the air; it feels so crazy good.

What’s it like touring now, given what’s going on in the world?
It’s really hard. Sometimes you just feel like you’ve had the s— kicked out of you; we don’t pretend that we don’t feel heartbroken. … We make music to try to make other people feel good. It makes us feel good too, but you know, there are days when we live off the energy that the audience makes. And without the audience there is no us.

How does case/lang/veirs fit into your overall body of work?
I feel like I’m just learning from these incredible musicians. I’d like to go from being a journeyman musician to being a great musician, and I think that takes a lot of time. … k.d. and Laura both have their own skills, and it’s really incredible to watch the way they lead things. Because it’s so easy to take your own band for granted, and to be so used to being the boss and to having things go your own way.

Lincoln Theatre, 1215 U St. NW; Wed., 8 p.m., sold out; Thu., 8 p.m., $59-$79.

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