Martin Scorsese has always been a huge Stones fan. Their songs have top billing in many of his movies. “Gimme Shelter” or “Jumpin’ Jack Flash” adds the right kind of menace and intensity to a pivotal moment in the story. Yes, somehow this group, once upon a time Little Boy Blue and the Blue Boys, is not out of place in the underworld of mobsters and murderers.

“Shine a Light,” the latest Stones/Scorsese collaboration is a bit different than “Goodfellas” or “Mean Streets.” The model is Scorsese’s “The Last Waltz,” the greatest concert movie that will ever be made. But the Band and all their friends in 1976 is a very different proposition than the Stones in 2007. The Band, weary of touring after 10 or 15 years; the Stones, going strong after 45. Forty-five years as the biggest band in the world does something to you. You bear little resemblance to your former self. The Stones of 2007 don’t sound very much like the Stones of 1977 or 1967. It’s not such a bad thing, as this album proves. But you’ve been warned.

Not having seen “Shine a Light,” I’ll stick to the soundtrack. I’m sure Mick Jagger does a lot of prancing and posing and jumping around, belying the fact that he’s 65. Yeah, yeah. He works out all the time. Big deal. Sixty-five isn’t that old. The music is what counts.

Much of the music is very good. The band sounds extremely professional; they’re certainly better musicians than they were in the ’60s. Charlie Watts is still the greatest drummer in rock and roll, the most precise, the most subtle. Most other drummers sound like neanderthals compared to him. His drumming is Apollonian. Watts and Darryl Jones are a great rhythm section, right up there with Watts and Wyman. Jagger’s voice is strong and tight, though he sings several of the songs in a lower register than before. The guitars sound good, too, though Keith Richards’ technique is flagging a bit. He plays the same twangy little solo on each song, no matter the song, and seems to relish it. I feel like he could do better if he cared to. Their sound is filled out by countless back-up singers and a horn section. One prefers not to think about these things.

The band sounds best in the rockers. “All Down the Line,” “She Was Hot” and “Live With Me,” a duet with a tackily excellent Christina Aguilera, are red-hot. The band unearths several songs off 1978’s “Some Girls,” their stripped-down, punkish, New York album. “Shattered” is transformed from goofy New Wave into a high-energy rocker. Their revision of their revision of the Temptations’ “Just My Imagination” is fantastic: The tight, sexy groove reminds you that the Stones can be one of the best dance bands. They even revive the campy country ballad “Faraway Eyes,” a song one would have expected to be buried forever. “Some Girls” rocks, but the line about black girls wanting to “get fucked all night” seems to have gone missing. No comment.

Richards croaks out three songs. “Connection,” from 1967, is a catchy throwaway piece of proto-punk. “You Got the Silver,” off 1969’s “Let it Bleed,” is imbued with a pathos only latent in the original. His voice is evidence of the ravages of his infamous life, but it is also one of the few indications of authentic feeling on the album. “Little T & A” — I’m going to take a stand here — is a great song.

The requisite blockbuster hits like “Start Me Up,” “Satisfaction” and “Paint It Black” are the least successful songs on “Shine a Light.” They sound uninspired and bloated, grandiose and prosaic at the same time, and it’s hard to hear the great songs underneath. “Loving Cup,” a song hidden deep within their 1972 masterpiece “Exile on Main St.” is given an unsatisfying rendition with Jack White. I appreciate the effort, though. “Tumbling Dice,” perhaps the greatest song of all time, and Keith Richards’ recent response to the question of which song best encapsulates his philosophy, is sadly given a half-hearted, tossed-off performance.

All in all, though, a very satisfying record. The Stones should search out the treasures in their absurdly extensive catalogue rather than playing the hits to death.