The rare sequel that improves on its predecessor, “Get Him to the Greek” also confounds the awful expectations you might get from its trailer. Actually Nicholas Stoller’s follow-up to “Forgetting Sarah Marshall” is only a semi-sequel, taking a supporting character that was the funniest thing in the earlier movie and elevating him to one of the leads in a buddy-road tale that gives a rock-and-roll spin to a pretty familiar story.

The plot centers on Aldous Snow (Russell Brand), the whacked-out British rocker Sarah dumped her boyfriend for in the original. He’s now a has-been, his last album “African Child” having been termed the worst thing to happen to the continent since Apartheid and his seven-year mate Jackie Q (Rose Byrne) having moved out with their son Naples (Lino Facioli). In Los Angeles, Aaron Green (Jonah Hill), a hapless drone at Pinnacle Records, proposes to his hard-driving boss Sergio Roma (Sean Combs) that they lure Snow out of his alcohol-and-drug sodden seclusion for a comeback concert at the Greek Theater. Roma agrees and sends Green to London to accompany the uncontrollable singer first to New York for an appearance on the “Today” show and then on to L.A.

Aldous, of course, proves a totally obstreperous fellow with a mind—or libido—of his own, and the travel plans do not go as scheduled. Green is soon embroiled in the guy’s relentless cycle of drink, pharmaceuticals and lust. The situation’s complicated by Aaron’s recent breakup with his long-time girlfriend Daphne (Elisabeth Moss), an internist who wants them to move to Seattle for her residency, by Snow’s sudden desire to visit his estranged father (Colm Meaney), a guitarist in a Las Vegas show, and by Roma’s constant foul-mouthed interjections.

The trajectory of “Greek” is predictable—it’s like “The Sunshine Boys” with only one boy, and a bad-boy at that. It’s inevitable that Aldous and Aaron are going to bond through a series of misadventures. It’s also preordained that the big concert is going to occur despite all obstacles, and that it will change their lives.

But the fun is in getting there in a story like this, and here Stoller and his cast provide a surprising amount of it. To be sure, a lot of the gags are incredibly raunchy—the sexual stuff can be a bit much, and there are entirely too many vomit scenes for anybody’s taste. But the good easily outweighs the bad. The picture gets a lot of mileage sending up not only the entire rock-and-roll business but so-called entertainment reporting, too. In fact, the opening segment, showing the precipitous fall of Snow as a result of his debacle album, is a slyly pointed satire on the very programs (TMZ, Extra and the like) featured in it. The “Today” show segment, moreover, might have been made in collaboration with that program, but it makes the supposedly news-oriented show look like a hack job.

And the leads make a good pair. One might fear that Brand would be a one-trick pony who would soon outlast his comic usefulness, and though he’s doing the same shtick familiar from his earlier pictures, it’s doled out with sufficient care that it doesn’t get tiresome. Hill, meanwhile, tones down his customary over-the-top persona; he has a few scenes where he cuts loose, of course, but generally he underplays to good effect, as in his scenes with Moss. There’s strong support from Combs, who shows he can rant with the best of them; from Meaney, who revels in playing a liquored-up lout; and from Byrne, who transforms credibly from spangled bimbo to superstar.

Even more important, the movie isn’t all goofy comedy—it actually has an undercurrent of drama and warmth. The Aaron-Daphne relationship is often funny, but it possesses some depth as well, and Snow’s darker side is periodically revealed, most notably in his meeting with his father and in his attempt to reconnect with Jackie. The latter sequence also includes a brief meeting between Aldous and Naples that touches on some serious issues and, despite the obligatory humorous elements, is actually rather poignant. Stoller matches his generally sharp script with direction that’s mostly assured, going into confused frantic mode only occasionally. He’s aided by Robert Yeoman’s crisp cinematography and the editing by William Kerr and Mike Sale, which are especially helpful in the “journalistic” montages and music videos, where the songs, presumably cobbled together by Stoller and composer Lyle Workman, do a good job of approximating the catchy tunes and ridiculous lyrics so common in the trade.

“Get Him to the Greek” is far from innovative and ever farther from subtle. But it’s one of the more genuinely enjoyable products to come out of the Apatow factory.