The Rolling Stones’ “Live Licks,” a collection of songs from the band’s massive 2002-2003 world tour, finds a different but successful way of encapsulating the band’s work. The first CD features the Stones’ best-known (and arguably best) songs, and though the second compiles more obscure tracks, it is a much more interesting listen.

After releasing 2002’s “Forty Licks,” their most thorough greatest-hits compilation, the Rolling Stones embarked on a massive world tour. Claiming that they wanted to combine the experience of arena and club shows for their audiences, they played a wide variety of venues — from gargantuan stadiums in Europe to the comparatively infinitesimal, and much more atmospheric, Roseland Ballroom in New York City.

The collection admirably attempts to recreate the interesting balance of the tour. But by putting their most famous tracks mostly on the first disc and deeper album cuts on the second, that happens in an obviously delineated manner.

Throughout both CDs the Stones sound very good, performing surprisingly well considering they’ve been together for more than 40 years (Mick Jagger and Keith Richards are both over 60).

No one would ever accuse the Stones of not enjoying what they do — they’ve certainly got the money to quit when they want — but on this recording they also sound happier than ever to be the Stones. On “Everybody Needs Somebody to Love” (a song made famous by the Blues Brothers), Jagger wails to the audience: “I’m so glad to be here tonight, so glad to be in your wonderful city,” and he sounds entirely sincere. Though it sounds like the first or second song of a night, it is ironically the last track of the second CD — which exemplifies the random order of songs on “Live Licks.”

This verve, combined with the impressively sharp sound of the recording, gives the collection a sharpness that is rare in most live albums.

One could complain that there is only one track from records after 1981’s “Tattoo You” (“You Don’t Have to Mean It” from 1997’s “Bridges to Babylon”). But considering the generally uninspiring and comparatively poor quality of their recent studio albums (recent meaning the last 20 years), this isn’t a tragedy.

And though it is hard to touch all the important bases of such a long and illustrious career, it’s a pity that there are no songs from their masterful 1967 “Between the Buttons.” The gorgeous ballad “She Smiled Sweetly,” which was performed at many of the smaller venues, would be a brilliant addition. Though to be fair, “Buttons” doesn’t have quite the same hard-rock feel as the work that came afterward.

From “Brown Sugar” to the ubiquitous “(I Can’t Get No) Satisfaction,” the first disc of “Live Licks” is a solid assortment of big hits recorded in concert. For the most part the songs are straight-ahead recreations that tap into the original versions’ greatness (the notable exception is “You Can’t Always Get What You Want,” which upsettingly lacks the children’s choir at its beginning).

But because it only has 10 tracks, the disc fails as a live best-of collection — which it certainly aspires to — inevitably omitting many of the highlights of the Stones’ massive catalogue. It may well have been called “One Quarter of ‘Forty Licks’ Performed Live.”

Thankfully, the second disc — a mix of fan favorites, lesser-known band favorites, and covers — is more interesting. Its highlights are lesser-known songs from classic albums like “Let it Bleed,” “Sticky Fingers” and “Exile on Main Street.” Taken together, songs like “Monkey Man” and the jammy, 10-minute-long “Can’t You Hear Me Knocking” provide a valuable showcase of the Stones’ best days.

Interestingly, two songs from the second CD are sung by the raspy-voiced Keith Richards, including a mediocre cover of Hoagy Carmichael’s “The Nearness of You.”

Of course, the Rolling Stones are no foreigners to the live album. 1969’s aptly-titled “Get Yer Ya-Yas Out” is one of the most exhilarating (and famous) concert records in rock history. Though “Live Licks” doesn’t compare to “Ya-Yas,” it certainly has the same energy.

Similarly, while there is nothing here uniquely astonishing, and while the collection is something of a live alternative to “Forty Licks,” “Live Licks” admirably balances the band’s classics with their lesser-known, though equally worthy, work.

And they sound great for 60-year-olds.