“We're still a small band,” Dawes frontman Taylor Goldsmith insists. “We've still got a long way to go before we are, like, 'This is a secure position for us.' ”

He's sitting outside the tiny Sqirl cafe on the seedy border between Silver Lake and East Hollywood, hunched over a wooden box that doubles as a breakfast table for him and Dawes' keyboardist, Tay Strathairn. His clothes are thrift-store anti-chic and his hair looks like it hasn't seen a comb in weeks.

But Dawes has been making big moves lately. The quartet Rolling Stone loves for its “twangy folk rock” played 14 showcases at the recent South by Southwest. They're about to go on tour with Bob Dylan. They hired big-shot producer Jacquire King (Norah Jones, Kings of Leon) to record their third album, Stories Don't End, which comes out April 9 on their own label, Hub Records. And they've signed with Q Prime, the powerhouse management company whose clients include The Black Keys and Metallica.

Goldsmith, Dawes' singer and guitarist, is an unlikely standard bearer for a 21st-century classic-rock revival: the Malibu-raised son of a former funk-rock singer (Remember Tower of Power? One of those guys.) who got his start playing angsty post-punk with Simon Dawes, a band that once opened for Incubus. Goldsmith prefers to describe himself as “born in Tarzana, grew up in Glendale.” (His family — including his younger brother, Griffin, Dawes' drummer — moved to Malibu when he was 11.) In person, he's earnest, slightly awkward and almost compulsively humble.

“I wrote 'Just My Luck' in, like, an hour,” he mentions almost sheepishly, referring to the prettiest ballad on Stories Don't End. “I've never done that with a song — I've always taken at least a week. I really just powered through it for the sake of being able to tell myself, 'OK, you can write faster sometimes.' ”

Most of Goldsmith's tunes feel like things meticulously labored over — in the digital age, a good Dawes song is a handcrafted objet d'art. Harmonies rise out of the choruses with the precision of a vintage watch. His lyrics feature the wit and economy of a great short-story writer. “You can put 'em on the counter there with all the other flowers/And help me figure out how to turn off this TV,” begins “Bear Witness,” about an old man who has just lost his wife.

Goldsmith takes his songwriting cues from the greats: Bob Dylan, Joni Mitchell, Warren Zevon. “I feel like what they're best at is taking some mundane, small experience and trying to carve out the human condition within it.”

Early in their career, Dawes name-checked Laurel Canyon in their press materials and played alongside Jackson Browne. But they now seem determined to recast themselves as a more modern band.

“It turns out it's 2013 and we're from now,” Strathairn says, munching on a roasted beet. He's leading-man handsome under his Yankees cap, with the same angular jawline as his actor father, David. “It's not like we're dealing in antiquities and re-enactment.”

Still, not all retro comparisons are unwelcome. “I got a couple of Steely Dans,” Goldsmith notes, referring to early press reactions to “From a Window Seat,” Dawes' latest single. “I was really happy about that.”

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