The New York Dolls, even more than the other overlooked legends who have reunited to enjoy overdue prestige (the Pixies, Mission of Burma, Dinosaur Jr.), are a band that missed its own moment. “Too Much Too Soon,” the title for its 1973 (and until now seemingly final) album about sums it up: The Dolls were too far ahead of their time to capitalize on their own innovations.(Punk and hair metal are but two of the genres that couldn’t have existed without them.) But then it’s never too late: Today the Dolls release their first new album, “One Day It Will Please Us To Remember Even This” (Roadrunner), in 32 years.

There really was no New York City music scene to speak of in the post-Velvet Underground vacuum of the early 1970s. For a few glorious and debauched years the Dolls ruled the wasteland in style. Back then, you couldn’t play clubs unless you were signed to a label or playing covers.The Dolls were neither, so they ended up at the Mercer Arts Center, a complex for off-Broadway theater and video shows in Greenwich Village. Playing every Tuesday night in the Oscar Wilde room, they inherited the in-your-face attitude of Iggy Pop and the theatrical androgyny of British glam stars like David Bowie and Marc Bolan.

In makeup, sparkly spandex pants, and Aqua Net-ed hair, the Dolls looked like a street gang in drag.They were led by David Johansen, a monstrous Mick Jagger doppelganger with a gaping mouth, needle-thin legs, and a talent for stylishly delivered lines: “When I say I’m in love you best believe I’m in love, L-U-V,” he pouted in the opening to “Looking For A Kiss.”

At the time, the Dolls’ sound was as messy and hard to pin down as their style: a footloose admixture of early rock ‘n’ roll, blues, ragtime, doo-wop, and roaring guitar licks reminiscent of the MC5.There’s an incredible amount of musical DNA crammed into their self-titled 1972 debut, bits and pieces of everything from Television to the Ramones, the Talking Heads, Joy Division, the Replacements, and Guns N’ Roses. It’s no wonder they didn’t catch on in their own time: It took other bands decades to unpack and flesh out everything the Dolls were up to in 1972.

The Dolls’ impact was felt most immediately in the emergent New York punk scene, but it came along a little too late to save the band. By the mid-1970s, they had imploded in a Malcolm McClaren-orchestrated spasm of red patent leather and faux-Communist idiocy.

But their merciful breakup in 1975 wasn’t the end of the story. Inimitable (few haven’t tried) axeman Johnny Thunders and drummer Jerry Nolan carried the torch into the punk era with the Heartbreakers, which produced the glorious (but again poor-selling) punk-classic record “Like a Motherf–r.” But the band would be short-lived: both former Dolls were by then serious heroin addicts (they would die, far too young, of health complications in the early 1990s).

Johansen soldiered on, but the highlight of his chameleonic post-Dolls career was “Hot Hot Hot,” the inexplicable camp hit he scored with his nightclub alter ego Buster Poindexter in the late 1980s. And who can forget him as the ghost of Christmas past in in the Bill Murray comedy, “Scrooged”?

More recently, Johansen has been recording roots music with his band the Harry Smiths, named after the eccentric folklorist, and growling Howlin’ Wolf covers alongside original Wolf sideman Hubert Sumlin. In 2004, the surviving Dolls (sans the late Thunders and Nolan; bassist Arthur “Killer” Kane died of leukemia in 2004) reunited to play the Meltdown Festival at the invitation of former Smiths front-man Morrissey, who was president of his local chapter of the New York Dolls fan club as a teenager. They’ve been playing intermittently ever since, to the delight of fans who never saw them the first time around.

But a new album is a gift to be greeted warily.After all, what does it mean to be the Dolls 32 years later, with only two original members? The band seems to share our anxiety: Even the title is an attempt to manage expectations.

But at 56, Johansen has become one of those unholy rock ‘n’ roll creatures who never seems to age.He sounds even better. The Dolls have always been, at root, a blues band, and Johansen’s gruff vocals suit the band well.

He’s also aged as a songwriter. Before, the Dolls were aspiring rock gods, their only altars the heathen ones of rock ‘n’ roll. Now an eclectic spirituality pervades many of Johansen’s lyrics. On “Plenty of Music,” he quotes from a Native American legend: “Don’t you destroy the song/cause when the song is gone/you’ll be gone too.”

It’s wisdom he applies to the reconstituted Dolls: you can hear them playing it safe, trying not to wreck the legacy rather than extend it. But doing so is its own kind of infidelity. The young Dolls never would have tolerated such cautiousness.

The up-tempo songs manage not to embarrass.Well, mostly: “Dance Like A Monkey,” the first single, is a silly song that takes up the evolution debate as a way to pick up a “pretty little creationist”; “Dancing On the Lip of a Volcano” is even stupider than the name suggests, despite a nice cameo by Michael Stipe. But “Runnin’ Around” captures a bit of the old gender-bending magic as Johansen recalls “watching gay boys get all the good seats.” Better still is “Gimme Luv and Turn On the Light,” a swampy, stomping blues — performed with an inconspicuous Iggy Pop — that sounds like a hell-bent version of an R.L. Burnside song.

Inevitably, the best songs are those that sound nothing like the Dolls of old because they escape impossible comparison.Johansen is a croaking Bob Dylan-sound-alike on the waltzing “Maimed Happiness,” with weary lyrics to match: “I doubt that I’d want to live this wasted life over again,” he sings against a spare arrangement of piano, electric bass, and drums.

But the highlight is “Take A Good Look at My Good Looks,” a song of fond remembrance that sounds like the other Heartbreakers, Tom Petty’s band. At a three decade remove, the “noisy years … sound like moments.”The present is equally fleeting. The song is Johansen’s way of saying farewell: “Take a good look at my good looks, then close your eyes/keep the picture in your mind, cause I’ll be gone.”

Unfortunately, the Dolls worth remembering already are.