Edie Brickell & New Bohemians rocketed from Dallas-based jam band to MTV favorite in before anyone had seatbelts locked. The group, fronted by singer-songwriter Brickell with her fragile good looks, enjoyed ample radio airplay (especially “What I Am”) and more than two million sales of its debut album “Shooting Rubberbands at the Stars.”

That was the late 1980s and 1990. The band amicably split when Brickell moved to New York, where she has recorded periodically and raises two boys and a girl with her husband of 14-plus years, icon Paul Simon.

Brickell, now 40, regrouped with New Bohemians on a surprisingly strong album, “Stranger Things.” The band’s tour will stop in Madison on Tuesday. She sounds comfortable and happy – and, when asked, notes that her daughter, age 11, took the group’s promotional photo.

Question: Is there an audience left for the band?

Brickell: We have a bit of an audience left. When we play now, there’s a sense of familiarity and goodwill. It’s not the same kind of buzz or energy that MTV provided all those years ago. I feel relieved that it’s not that way. It’s more of a slow-burning fire that feels better to us.

Question: Is reuniting with New Bohemians something you expected to happen?

Brickell: We didn’t really reunite so much as we made a record publicly. When I went back to Texas to visit my family, I would visit the band and we would jam. We collected these songs over the years.

Question: You’re playing a mid-sized club here (Annex), but it seems like you’re as content to play a club as a big theater. Is that true?

Brickell: Now more than ever, it’s a lot more fun to play. We made the record we wanted to make. Years ago when we played, it was less about the record and more about being a band someone had seen a video relating to a TV personality rather than the music. This feels better. It’s liberating to go out and play.

Question: Do you look back fondly on your window of fame in the late ’80s and early ’90s?

Brickell: It was a real mix. When we played clubs in Dallas, I couldn’t wait for the days when we get on a tour bus and hopefully get our record on the radio. Then when it happened, there were so many people in our lives. People trying to direct us. I was a wallflower growing up. When it went national, there was a little bit too much attention.

I basically just hung out in my hotel room and tried to figure out happiness. I wasn’t getting it from that attention. I was 22 at the time. I was really insecure. I wanted to have real love in my life as opposed to love of an industry or an audience. (Fame) was good because I did meet my husband because of our sudden success. He took notice of me based on that record. That was fantastic.

Question: Does Paul sing around the house?

Brickell: He sings a little bit. It’s mostly ’50s doo wop. In the car, we both sing. If I start singing something then he’ll jump in and harmonize. Man, it’s so beautiful. He sounds great with anybody. That’s always a joy to hear.

Question: Do you play him your songs for feedback?

Brickell: When I first write a song, I’ll catch myself singing it all the time. If he walks in and says, “Oh, that’s a cool song. Who does that?” That’s a thrill.

Question: When you co-wrote “What I Am,” did you think it would become such a big hit?

Brickell: I had no clue. There have been songs that I’ve liked more than that song. And I thought, Everyone’s going to like this song,’ and no one did.

Question: What about something as observational as “Circle”?

Brickell: That seems to get more response from the audience when we play after all these years (than “What I Am”). There’s a deeper emotional connection to that song. The other one is fun, but people hoot and holler when “Circle” is played.

Question: What will surprise people who go to the show?

Brickell: We’re more joyful because we are older. The self-consciousness is way in the backseat. It’s not completely dead. It’s part of being a performer. Before it was just painful. Now we’ve learned to let go and feel free in the music and have a good time.

Question: Did turning 40 (last May) cause any reflection?

Brickell: I’ve always been too reflective. It made me want to appreciate all the people and all the good things around me. I have looked at all the darkness a lot and tried to study it and understand it. Now I’m thinking, “It’s time to check out the obvious beauty that is all around.” And express it without being corny.