The day after headlining Webster Hall in New York, the Haim sisters hoist their equipment out of a black van and lug it across a sidewalk to the entrance of WNYC, which is kind of like the Big Apple's KCRW. Alana, 21, Danielle, 24, and Este, 27, in matching black motorcycle boots, are double-booked this afternoon, with back-to-back performances and interviews on two different programs.

At this point, they are used to being in demand. It took the band five years to finish its debut album, mainly because the Haims kept getting invited out on tours they couldn't turn down: Vampire Weekend, Rihanna, Florence and the Machine, Mumford & Sons and, most recently, Phoenix. And they still had to decline some offers, like when A$AP Rocky asked them to be his backing band.

On the strength of the EP they released last year, Haim booked slots at both Glastonbury and Bonnaroo, and won praise from everyone from Katy Perry to The New Yorker's Sasha Frere-Jones. Their debut full-length, Days Are Gone, is finally finished, and sees release by Columbia Records on Sept. 30.

New York City, of course, is a long way from Valley Village, the tiny San Fernando Valley town they grew up in, but there is something about the way each of them carries their instruments up to the seventh-floor studio that makes them look, even in their badass boots and leather jackets, like the kid musicians they used to be.

Even then, they were a close-knit trio. Their parents used to leave Este in charge of Danielle and Alana, with orders to practice the classic-rock covers they played for their family band, Rockinhaim. In addition to Danielle on guitar and Este on bass, it also featured Dad on drums, Mom on lead vocals, and Alana, age 4, on the cow bell. They played their first show at Canter's Deli on Fairfax, before graduating to gigs at religious festivals and county fairs.

“We'd agree, OK, we'll tell Dad we practiced for an hour, and then we'd watch TV,” Alana says. As soon as they heard his key in the lock, the three would snap into action, shutting off the TV and patting it down for static, Este says, “ 'cause my dad would come home and feel the TV and be, like, 'Did you guys practice? Were you guys watching TV?' ”

Back in those days, they would go to Fashion Square to buy Spice Girls Chupa Chups lollipops from Limited Too. One time after a Rockinhaim gig in Sherman Oaks, Este and Danielle were approached to be part of their own Spice Girls knockoff, called The Valli Girls. The songs they sang landed on soundtracks for the Trollz doll TV show and Sisterhood of the Traveling Pants.

When they were older, Este and Danielle left Alana behind, sneaking out to shows at Spaceland, Sixth and Alameda Warehouse or the Smell. Este explains now, almost apologetically, “I could only find one fake ID, and getting Alana a fake ID when she was like 13 … ”

“It was hard with my braces,” Alana agrees.

Five years ago, when Alana was finally in high school, the three of them began playing shows as Haim. Critics have struggled to describe the band's sound, often falling back on a weak comparison to Fleetwood Mac, and that's partly because they draw from such a wide landscape. Days Are Gone is like a found poem of L.A. radio sounds — smooth R&B vocals, blistering classic-rock guitar riffs, punchy '80s pop drumbeats. “People ask us, 'What did you grow up listening to?' and we're, like, 'Just L.A. radio,' ” Danielle says.

Seriously, though. “People don't get how dope it is,” Alana adds. They cite KRTH 101, first and foremost, but they also love KIIS. (“My dream is to meet Rick Dees,” Alana says. “And sing 'Disco Duck' with him?” Este asks. They harmonize: “Discooooo, disco duck.”) Then there's KDAY, Power 106, KLOVE, The Wave (they sing that jingle, too), KCRW, of course, and 100.3 The Sound.

Ironically DJs in the U.K., not L.A., gave Haim their early radio play. Cuts from their EP started showing up on BBC's Radio 1 not long after the band played at South by Southwest in 2012.

“They started playing [our song] 'Forever' before we were even signed, and before we knew it we were selling out 500-capacity venues [in the U.K.] — and in L.A. we were playing, you know, the Echo,” Danielle says.

If you watch YouTube videos of Haim at South by Southwest that year, it's striking how much they've grown as a band since then — they were wilder, noisier and rougher around the edges in those performances. But it's even more striking how close those songs are to the cuts that appear on the finished album.

Days Are Gone is the right title for a record characterized by both a casual nostalgia and an acute sense of loss. It's about growing up. It's a record of the time they spent making it, too — like a doorjamb marked with their heights over the years.

“The Wire,” the single they released this summer, is a good example of how the album grew up with them. It was originally written back in 2008. The sisters rerecorded it every year since then, sometimes three times a year, until they got it right.

“It's kind of a hard song to record because it's basically all major and it's a shuffle,” Danielle explains. “It turned into maybe something too sweet sometimes, or kind of too sugar — I don't know. Every time we did it, there was an issue with it.”

Eventually they figured out the right combination of sample beats and live percussion.

Hearing the album version was gratifying not only because it had been a tricky one to get right, Alana says, but “ 'cause there was also kind of fear that we would never really be proud of it.”

Turns out they shouldn't have worried. When it was released earlier this summer, “The Wire” exploded online, raising Days Are Gone's buzz. Not that they've had time to notice.

“Did it explode?” Alana asks, genuinely surprised. In fact, its success helped the band sell out Webster Hall the night before.

Backstage, the Haim sisters will happily reminisce about their days growing up in the Valley, working at Wasteland (Este), Crossroads Trading Company (Alana) or American Rag (Danielle), and cramming, with 47 of their closest friends, into a Palm Springs hotel room for Coachella.

It's clear when they take the stage — even a small, studio stage like the one at WNYC — that those days are gone. Any trace of naivete evaporates as they launch into a searing rendition of “Falling,” from the new album.

Out there the soft-spoken middle sister, Danielle — who tends to hang back in interviews, ceding the floor to her sisters — commands the spotlight. But they perform as a unit, lost in a kind of hypnotizing psychic sync.

Their entourage, looking on from backstage, is their old Rockinhaim bandmates: Mama and Papa Haim. While the band performs, their mother whips out a bejeweled phone and flips through pictures of the previous night's show, pausing on one of their father out in front of Webster Hall, beaming proudly, pointing at their name up on the marquee.

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