Give the people what they want — it’s a maxim that applies to veteran pop musicians as much as it does to election campaigns. Critics celebrate innovation, experimentation, and vision, but pop music, at its core, is a conservative medium, and most fans want what they fell in love with in the first place. And that patina of consistency is what makes the new albums from Madonna and Portishead, both out today, such delectably safe bets.

The bad news about “Hard Candy” — Madonna’s first new album since 2005’s “Confessions on a Dance Floor,” the 11th of her career, and the final piece in her contract with longtime label Warner Bros. — is that the lead single, “4 Minutes,” defines the album’s approach. The song, which was produced by hip-hop/pop go-to man Timothy “Timbaland” Mosley and his equally pop-friendly protégé Nate Hills (aka DJ Danja), and features guest vocals from Justin Timberlake, is unabashedly mainstream dance pop that sounds like everything else on the radio. Or maybe that’s the good news.

Thanks to omnivorous pop producers such as Messrs. Mosely and Hills, and the ubiquitous Pharrell Williams (who also produces a number of “Hard Candy” tracks), contemporary pop these days is more dance-music loose than it’s been in decades, with beats, breaks, and textures as likely to come from hip-hop and hard-core underground dance music as from middle-of-the-road pop and rock. Messrs. Mosely and Hills’s backing beat for “4 Minutes” borrows the marching-band motifs that buffered recent standout tracks from rappers Rich Boy (“Boy Looka Here”) and Young Buck (“Get Buck”).

For Madonna, though, this characteristically ground-shaking beat feels too static and robotic, as if the 49-year-old ex-Material Girl is trying to shove a college football halftime show into a techno track. Madonna hasn’t sounded this out of place inside a pseudo-dance beat since 2003’s “American Life,” which was largely dismissed by critics and the public alike.

The good news about “Hard Candy” is that “4 Minutes” is one of only two or three misfires on a fascinatingly mainstream big pop album. It’s the sort of widely appealing album that Madonna hasn’t really made since the 1980s, and it’s one of her most immediately pleasing in years upon first listen.

Void of quasi-political message songs or vaguely confessional lyrics — which hung like millstones around “American Life” and portions of “Confessions on a Dance Floor” — “Hard Candy” is the dance-and-feel-good-about-who-you-are Madonna of “Get Into the Groove.” On past albums, Madonna seemed to bend various dance-music producers to suit her musical will, but on “Hard Candy,” it sounds as though Messrs. Mosely, Hills, and Williams were authorized to define each song’s production, forcing the star to find a way to make it her own from the inside.

And to her impressive credit, Madonna does just that. From the bump-and-grind crackle and tease of opener “Candy Store” to the familiar master-slave leitmotif pumping through the head-bobbing closer “Voices,” “Hard Candy” still feels like a Madonna album, even though, from a strictly aural standpoint, it could be anybody singing. In a way, it’s a typically audacious move by Madonna. Since 1998’s “Ray of Light,” a terrifically successful album that provided something of a “comeback” for Madonna at age 40, she has worked with some of the more forward-thinking producers in dance music to turn out albums that sound like little else in pop. For “Hard Candy,” she has turned to the artists behind a wealth of what has defined dance-pop this decade, producers who created an album that sounds like fairly typical dance-pop. But Madonna nevertheless makes it her own.

That certainly is the case on the disco-fied hip-hop of “Give It 2 Me,” “She’s Not Me,” and “Beat Goes On,” the last of which is especially silly but effective. Mr. Williams dishes out one of his characteristically sparkly pop productions for the song, a casual funk beat tempered by tinkling keys. Madonna sings almost like a house diva, her lyrics simple and recurring — a basic call to dance — as though the song is waiting to be turned into an extended remix. At the 3-minute mark, Kanye West emerges out of this understatedly funky backdrop with a wonderfully superficial guest rap, and Madonna herself serves as the hype-woman, providing verse-ending shout-out “heys.” Even a mid-tempo ballad such as “Miles Away,” which could just as easily have become a backing beat for Gwen Stefani or Nelly Furtado, is transformed into an ethereally downy Madonna love song.

Make no mistake: “Hard Candy” is not “Ray of Light” (or “True Blue,” for that matter), but it’s quite entertaining to hear Madonna interacting with contemporary pop music instead of trying to define it. The album is playful, which makes it easy to forgive its clumsy missteps. Mr. Williams pairs a ragged Baltimore club beat with a flamenco guitar for “Spanish Lesson,” a bizarre song whose lyrics are literally what the title claims: “mucho gusto means ‘I’m welcome’ to you.” The song is verbally silly and musically schizophrenic, and it doesn’t work in the slightest. But Madonna hasn’t sounded this goofy since the early 1980s, and every 49-year-old should have this much fun experimenting in public.

***

“Third” (Island Records), the first new album in 11 years from the British electro-soul outfit Portishead, deftly threads the needle between change and not changing a thing. Musically, the album is a slightly different beast than 1994’s “Portishead” and 1997’s “Dummy.” Those two albums, downer mood swings as beloved during the mid-1990s as the Smiths and the Cure were in the mid-’80s, were built on plush, looping samples and laced with mournful organ lines and strings. Both were seminal documents in the trip-hop style, a fusion of acid-house and hip-hop that forged a darkly ruminative, rhythmically hypnotic form of down-tempo pop.

Which is exactly what “Third” is, even if the sounds and textures that Portishead’s principal song crafters (the producer and multi-instrumentalist Geoff Barrow and guitarist Adrian Utley) turn to are now noisier, more blunt, and more melodramatic. Electric guitars slice and buzz through the bubbling percussions of “Plastic” and agitate the stark mood of “Hunter.” Rippling, German dance-floor rhythms propel “Nylon Smile” and the album’s lead track, “Silence.” The lead single, “Machine Gun,” carves its staccato melody out of a techno throb interrupted and chopped into a martial goose step.

Still, all these extroverted sounds and beats collide to form a sound that moves to a faint pulse — and, as always, vocalist Beth Gibbons provides Portishead’s real melancholy. Although she has always been the band’s lone singer, Ms. Gibbons’s voice has never been Portishead’s dominant instrument. Her mid-to-upper-range register has always folded serenely into the band’s steamy sonic wallpaper, her warbling words providing the vocal loneliness to match the music. “Did you know what I lost? Did you know what I wanted?” she sings in an eerie chill on “Silence,” and it’s enough to turn the lights down on the song’s roiling beat. The self-lacerating doubt continues on the stark “Nylon Smile,” on which Ms. Gibbons barely voices “I struggle with myself hoping I might change a little / hoping that I might be someone I want to be,” before going on to wonder, “Looking out I want a reason to repair, ’cause I don’t know what I’ve done to deserve you.”

Even when the band dips into the derivatively lazy — specifically “We Carry On,” a blatant reworking of the Silver Apples’ “Oscillations” — Ms. Gibbons’s permafrost vocals coat the music with a pixie dust made from forlorn visions of dread and despair. As an album, “Third” doesn’t immediately pull its listeners into its emotional black hole, but since trip-hop’s late-’90s evaporation, such musical moods are in short pop supply. And the good news about the new Portishead album is that it’s cold enough for its longtime fans to warm to.