“If the Jonas Brothers‘ first moment on the cover of Rolling Stone found them reaching the height of teen pop stardom, their latest — on stands this week — finds them pushing for an even loftier goal: musical credibility. (Click above for exclusive footage from their new RS cover shoot.)

“I think we are working to make that trade without having to give anything up,” Kevin Jonas tells Rolling Stone in our cover story. (Check out photos from their Rolling Stone cover shoot here.) “But I think it will take time, because of where we came from. I would honestly say to anybody, if you were in a band like us, you would take advantage of those platforms too. It’s easy for people to say, ‘No, I’m a real rock & roller,’ but I think you do what you’ve got to do.”

Our Jenny Eliscu spent time with the brothers in Los Angeles as they prepared to hit the road in support of their most ambitious album yet, Lines, Vines and Trying Times. The album, the tour and much of what the band does these days seems designed to help facilitate the leap from teen pop to contemporary rock. It’s a challenging feat that few have pulled off. (Check out our look at artists who managed to outgrow their pop roots.) But the brothers are working hard on what they know will be a long, slow march to credibility. Eliscu found Nick on point as the band’s creative lead, putting their touring band through their paces (his brothers have started calling him “Mr. President”), while Kevin helps to steer the Jonas business and image (he even built a foam 3-D scale model of the band’s new stage set, which now takes 180 people to assemble at each show).

“We have an operation around us that we run,” Kevin tells Rolling Stone. “It’s not run for us, or dictated to us. Everything that we do, we sign off on.”

But even with a strong operation and a lot of hard work, the band knows that teen idols rarely make the leap to “serious artist.” “Personally, I’m not in the band to say, ‘Hey, you need to respect us, take us seriously,’ because that’s kind of stupid,” Joe tells RS. “We’re doing it because we love it, and we don’t care what age group we attract. If they like our music, they like our music, and if they don’t, fine. We don’t need you like our music.”

Jenny Eliscu’s Rolling Stone cover story, “Boys to Men,” is on newsstands now”

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