Rhett Miller is the frontman for rock band Old 97’s, a solo singer-songwriter, an essayist and a podcaster.

And he’s also a father of two, which indirectly led to his newest gig of picture-book writer. “No More Poems! A Book In Verse That Just Gets Worse” (Little, Brown, $17.99) is a compendium of wry kid-friendly verses on everything from sibling strife to the irresistible lure of screens: “I used to go to Mom’s house/With a birthday cake/Now I simply text her/Don’t even have to bake.”

The book’s roots stretch back several years, to the bedtime routines for his now-teenagers.

“I would pull out Shel Silverstein, Roald Dahl and Edward Gorey and we would read each other poems,” explains Miller, who will be at BookPeople on Monday. “There was something so interactive and immersive about it. We would talk about the characters in the poems. … I watched them fall in love with the humor and the intelligence in them, especially the Shel Silverstein poems.”

Fast-forward a few years and Miller was on tour and missing his kids. The usual phone check-ins didn’t always result in the best conversations, so he hatched a plan.

“I knew if I got them on FaceTime I wouldn’t be able to hold their interest, but if I went out and brought them a new poem to look at … I could trick them into spending more time,” he said.

A routine was born. He’d get up early, find a coffee shop and write a draft of a poem, which he’d then text to his kids. Post-school, they’d call in with their notes.

“Part of why it was so fun and so easy is that as I was doing it, I didn’t think of it as something that was going to become a commercial enterprise, which takes a lot of the pressure off,” he says. “I would say, ‘Let me have it, tell me what you really think.’”

They would, indeed. They liked when a poem assumed a certain level of intelligence and employed higher-level language. And they didn’t shy away from informing Miller, “No, Dad, this sucks.”

Indeed, Miller hasn’t escaped the universal challenge of seeming uncool to his kids. To wit, “Rock Star Dad,” written in the voice of Miller’s then-13-year-old son:

“One guy at the show/Got so worked up I thought he’d cry/I’m like are you kidding?/My dad’s such a boring guy/I guess I like his scrambled eggs/He gives a mean foot rub/But why must these fanatics/Pack themselves into the club?”

Expressive, energetic illustrations spring off the pages of “Poems,” created by Caldecott medalist and New York Times best-selling author and illustrator Dan Santat. The pairing had an unlikely beginning: Miller was listening to Sarah Enni’s “First Draft” podcast, which spotlights authors, and Santat was the guest.

“I thought, ‘This guy sounds so cool; he sounds like somebody I want to hang out with. I wonder if his stuff is any good?’” Miller’s editor indulged him with an ask of the much-celebrated Santat — who signed on to the project right away. Though they didn’t get to meet until after the proofs were complete, the two now tour together.

“I learned so much from the way he interacts with kids,” says Miller, who credits Santat with inspiring on-the-spot poem writing from audience contributions. “It’s so important to stress to the kids their own agency. Any one of them can do this. They can make art.”

And what do his in-home critics think of “Poems” now that it’s out in the world?

“Their voiced admiration is so grudging,” Miller jokes. “When the book came in and we’re sitting there with this hardback book and they both kind of let out this … noise: ‘Oh, my God, Dad, it’s real.’ I think that they had kind of always thought it was something we’d joke about, but it would never really happen.”