‘Rebels’ (1985)

Mr. Petty famously broke his hand in a fit of pique during the recording of the Heartbreakers’ 1985 album “Southern Accents.” That’s a high price for the music that resulted, but it was mostly worth it. “Rebels,” the ballad that opens the album, is uncharacteristically explicit about his ties to the American South — at times the lyrics read like his version of the Band’s “The Night They Drove Old Dixie Down” — but, true to form, any pride that’s there is undercut by darker notes of doubt and shame. It’s an unusual song, worth listening to if only for a fuller understanding of where he felt he came from.

‘End of the Line’ (1988)

On a break from the Heartbreakers, Mr. Petty ended up jamming in L.A. with his friends George Harrison, Bob Dylan, Jeff Lynne and Roy Orbison. Their 1988 debut as the Traveling Wilburys is mostly a curio for completists, but this gently swinging country tune is a gem that would have been a highlight among any of its participants’ solo releases that decade. The best part is the chorus, where a nonchalant Mr. Petty teases a former flame or friend: “Maybe somewhere down the road a ways / You’ll think of me, wonder where I am these days.”

‘Free Fallin’’ (1989)

“Full Moon Fever,” the solo album that Mr. Petty released in 1989, is his second front-to-back classic LP (the first was “Damn the Torpedoes,” a decade before). Several of its songs, including the pleasantly defiant “I Won’t Back Down,” the delightfully bizarre “Runnin’ Down a Dream” and a spot-on cover of the Byrds’ “I’ll Feel a Whole Lot Better,” are among his strongest work. But the best and most important song on “Full Moon Fever” is “Free Fallin’,” the Top 10 hit that jump-started the second act of Mr. Petty’s career. It’s essentially an update on “American Girl,” veering between awe-struck longing for the narrator’s dream lover and biting sarcasm toward the same. But it’s a much kinder song: This time, he’s self-aware enough to acknowledge his own role in breaking her heart, and to admit he misses her. “Free Fallin’” marks the moment when Tom Petty proved he could handle the ’90s.

‘Into the Great Wide Open’ (1991)

Mr. Lynne, who formed a close working relationship with Mr. Petty in the Traveling Wilburys and on “Full Moon Fever,” came along as a producer when the singer returned to the Heartbreakers fold in 1991. He’s the reason the group’s next album, “Into the Great Wide Open,” has that refreshed glow. The title track is an affectionate parable about a “rebel without a clue” named Eddie, who moves to L.A. and becomes a rock star. Everything seems to be going swimmingly, at least until the last verse, where our hero hears the words every major-label artist dreads: “Their A & R man said ‘I don’t hear a single.’ ” Mr. Petty makes you feel bad for the poor kid even as you laugh at his wry delivery.