“Tell all the truth but tell it slant.” Fox News thug Bill O’Reilly’s recipe for success? Nah. That would be a line from everyone’s favorite 19th-century diva, Emily Dickinson—a poetic dictum that’s been interpreted alternately as a statement of aesthetic principle and a boldfaced invitation to lie, at least a little.

The goofballs in indie-pop band the Caribbean could probably go either way. On its Web site, the far-flung but D.C.-based group presents itself as a buttoned-down corporate entity, complete with a smarmy mission statement, a wide selection of “products,” and a design scheme borrowed from Microsoft. Indeed, if you Google your way to the URL by accident, there’s a good chance you’ll be taken in. There’s even a link—hardy har har—for customer support.

The band’s music is similarly slanted. Multi-instrumentalists Matt Byars, Don Campbell, Tony Dennison, and Michael Kentoff have earned a ton of music-press kudos for their freewheeling take on traditional pop-song structures, which combines found sounds, unresolved chord progressions, and quavering vocals that sometimes sound so understated, you wonder if they’re being stated at all. True, the Caribbean occasionally flirts with normality: Its long-playing debut, 2001’s Verse by Verse, comes with a fistful of catchy tunes, some of which are only slightly mutated. But usually, just at the point when your average indie group would be content to insert Anthemic Chorus A into Guitar Drone B, the Caribbean chucks formula in favor of avant-meandering, more often than not wandering away from the main thread of the song and spooling out an entirely new one. Linear, in other words, these guys are not.

Album No. 2, History’s First Know-It-All, finds the group keeping up the weird work. The disc is a wacked-out assemblage of a dozen tracks that run the musical gamut from the really strange to somehow-even-stranger. Deftly placed musical allusions—a little Beatles here, a dollop of Brian Wilson there, and is that Burt Bacharach’s hair gel I’m smelling?—make it clear that the band knows the ins and outs of pop songcraft. But it’s just as clear that the Caribbean has zero interest in writing a straightforward tune this time out. Instead, History mostly offers tantalizing hints of what might have been if only the guitarist had coughed up an actual hook.

Or, for that matter, if the drummer had been in the same room as the bassist. On History, it turns out, he frequently wasn’t. The group’s four members live in three different cities, and though they have a studio in the District (wryly dubbed the National Crayon Museum), their recording process reportedly involves passing around sound files via e-mail. As a result, the new record sometimes has the disconnected feel of an Internet jam session, a hi-tech but frequently lo-fi musical exercise played out in asynchronous time.

Some tracks even sound as if they had dropped a data packet or two along the way. Disc opener “Oahu Sugar Strike,” for example, begins as a crusty pocket symphony, with Kentoff plunking out a riff on what sounds like a very loosely strung acoustic guitar. In the background, broken glass rattles and onionskin pages turn as Kentoff’s voice drifts hazily through the mix. “So you’re stateside now/Couldn’t help but feel dismayed,” he intones tentatively, apropos of—well, your guess is as good as mine. But just as you’re warming to the CB-radio sound quality of the whole rickety contraption, the band flips a switch and the track morphs abruptly into a slick but woozy psychedelic anthem worthy of the Flaming Lips. It’s even decked out with gorgeously tremoloed guitars and a microphone that sounds on the verge of shorting out.

That juxtaposition is arresting—and also a little atypical. More often, the Caribbean just plays in distinctly different styles simultaneously. “Officer Garvey” features a bracing guitar attack reminiscent of early XTC in the right channel and a demented keyboard romp reminiscent of strip-mall carnival rides in the left. On “Bulbs & Switches,” rumbling, jazz-inflected piano chords drone aimlessly behind a feisty drum machine that keeps strict time near the top of the mix. And though the best thing about “Fresh Out of Travel Agent School” is its title, the tune does sound-check both Bacharach and the Beach Boys via a cheesy, cocktail-lounge interlude and lush (if synthetic) orchestration. Elsewhere, the band serves up a ramshackle piano-plinked waltz called “The Requirements,” which sounds as if it were being broadcast from the great room of Disney’s Haunted Mansion. If it weren’t so damn goofy, the song would almost be scary.

Sonically adventurous though they are, each of those tunes makes the Caribbean seem like a new piece of Ikea furniture: All the pieces are there—maybe—but assembly is definitely required. When the band tightens the bolts, things get more than merely unböring. “It’s Unlikely to Settle the Difference” comes with an insistent melody and chiming guitars that move more or less in sync with the song’s seductive thunka-thunka rhythm. And though the disc’s ace title track opens with the ambient sounds of chirping birds and passing cars, those distractions give way to a bright, powered-by-live-drums pop song that some daring Clear Channel type should queue up right after spinning a little vintage Tears for Fears. Best of all, slow-motion set-closer “Check Kiting” floats by like a dream-pop cloud, one loaded up with the disc’s prettiest melody and, thanks to a riff borrowed from the Beatles’ “I Want You (She’s So Heavy),” its niftiest guitar part, too. Not even Kentoff’s Diazepamed singing can bring the thing down.

But even at its most accessible, the Caribbean could never be called conventional. The band is too reflexively experimental for that, too committed to skewing musical forms. That, of course, is a great pop tradition in itself. Just take the case of the mighty Devo, a pop band that more than lived up to its contrarian name. Ohio’s finest spud boys spent years dismantling and reassembling robotic disco rhythms before they finally got everything exactly wrong and scored big with “Whip It,” a twisted dance-floor classic of their own.

The Caribbean, on the other hand, hasn’t yet built its perfect product. On History’s First Know-It-All, the band frequently comes on like a lovable drunk: charming but incoherent. When it works, though, the disc isn’t just slanted—it’s also pretty darn enchanted, an ambitious undertaking with enough pop savvy to make you go diving for the catchy tunes beneath its experimental surface. CP

The Caribbean performs with Little Pink Saturday, March 8, at the Galaxy Hut, 2711 Wilson Blvd., Arlington. For more information, call (703) 525-8646.

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