After Green Day’s stunning success with 2004’s “American Idiot” — still the most important rock album of this century — the band started walking a narrowing tightrope.

Singer-guitarist Billie Joe Armstrong felt the band needed to continue addressing political issues while still crafting catchy pop-leaning punk, with ever-increasing stakes. But following the stress of the near-simultaneous release of three albums “Uno! Dos! Tré!” in 2012, it all came crashing down. Armstrong entered rehab and Green Day went on hiatus, staying out of the spotlight for years aside from getting inducted into the Rock and Roll Hall of Fame last year.

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The band’s new album “Revolution Radio” (Reprise) was done essentially in secret and, for the first time since 2000’s “Warning,” has no overarching theme. But the freedom to write whatever they want seems to have energized Armstrong, bassist Mike Dirnt and drummer Tré Cool to deliver plenty of great songs on a wide range of topics.

The stunning single “Bang Bang” disguises the demented view of a social media-obsessed mass shooter wannabe in a full-throttle punk rave-up and the super-sweet backing vocals of Dirnt and Cool. “I wanna be a celebrity martyr, the leading man in my own private drama,” Armstrong sings, before adding, “Bang bang, give me fame, shoot me up to entertain.”

Even more potent is “Still Breathing,” where Armstrong declares “I’m still alive” over the peppiest pop punk we’ve heard from Green Day in years. “I’m like a soldier coming home for the first time,” he sings, genuinely sneer-free. “I dodged a bullet and I walked across a land mine.”

“Revolution Radio” is definitely more wistful than its predecessors, whether nostalgically recalling a troubled youth in the chiming “Outlaws” or celebrating Armstrong’s wife in the jangling singalong “Youngblood.” It’s a testament to the artistic power of Green Day that its comeback album is so accomplished and anything but tentative.