Lately, indie rock has taken a turn toward the weird. Only a few years ago it was infatuated with the artful mimickry of retro rock. Now it celebrates bands who eschew obvious influences altogether. This was part of what fueled the fascination with the Montreal band Arcade Fire, who went from unheralded to inescapable in a matter of months. Now the same thing appears to be happening with Brooklyn’s own Clap Your Hands Say Yeah.

The band has been together a little more than a year, is still unsigned, and until recently was mailing albums from its members’ apartments (they’re now selling through Insound). Not long ago, a band at this nascent stage would have years of toil and econo-touring to look forward to before building a following of any size. Not so today. Thanks to local press raves and a word-of-mouth campaign that spread like wildfire, Clap Your Hands Say Yeah has become one of the hottest young bands around. David Bowie attended one of their recent shows – now crowded with A&R men for major and indie labels alike.

The attention is well-deserved. Still, it’s curious to find such consensus around such an unconventional sound. The New York Press called their music “the most captivating, Talking Headsesque bizarro pop you’ve ever heard.” Gothamist put it more simply: “This band is just really f-ing good.” Arbiter of indie taste Pitchfork agreed: “Basically we’re trying not to piss ourselves,” stated the review.

Clap Your Hands Say Yeah waste no time showcasing their weirdness. The first song, self-titled, on their self-titled debut album, begins with what sounds like an oompah-oompah organ warming up to play “Take Me Out To the Ball Game.” Then comes a naive xylophone; the organ again, quavering this time; handclaps; a ghostly chorus; and frontman Alec Ounsworth sounding like a delirious carnival barker.

It’s not that there aren’t recognizable influences in their music; in fact, there are many – it’s just they’re so scrambled that they’re not easily identified. In other words, it’s just the sort of intricate pop jigsaw puzzle indie-rock kids love to piece together. There are Velvet Underground-y sections of amorphous guitar, Modest Mouse bent-note squiggles, cacophonous Neutral Milk Hotel jams, lovely passages of Interpol-inspired gloom, Modern English pedal effects. But the most overt and probably accidental reference is Ounsworth’s voice, which has a topsy-turvy, 2-D quality much like David Byrne’s.

The lyrics are equally patchwork and jumbled. Their innate dreaminess is magnified by Ounsworth’s mumbling delivery. The results, when you can make them out, are often enticingly enigmatic: “Tattered dress, sunburned chest / You will pay for your excessive charm”; “All that we have salvaged from the fire / Was a waste of time”; “Time has gotten by on alibis and charm.” They’re almost aural inkblots, which may be the key to their success: you can read into them whatever you want.

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British songstress Emma Louise “Scout” Niblett likewise owes her modest success to indie rock’s indulgence of the willfully bizarre. But as her headlining set at the Knitting Factory on Friday night showed, she’s her own favorite audience and worst enemy.

Niblett is currently touring behind her new Steve Albini-produced album “Kidnapped by Neptune” (Too Pure), and drew most of her material from it. The songs fell into two distinct, warring, camps: one absorbing, the other rather annoying.

The first involved her singing eerie, drawn-out lines against delicately strummed electric guitar. In such moments, her voice took on a magical quality reminiscent, alternately, of Bjork and Cat Power’s Chan Marshall.

It managed to elevate her material, turning a picayune song like “Pom Poms” – “Does anybody know a cute girl with some pom poms?” – into a mesmerizing high school fairy tale. An entire concert in this mode would be spellbinding, but Niblett is determined to break her spell even before it can take hold.

Her second mode reverses the formula of the White Stripes: A man crashes out rudimentary beats on kick drum and cymbals while she plays the Jack White role on guitar. Unfortunately, she has none of his rock-god magnetism. Dressed in an alert-orange road worker’s vest, playing fuzzy Nirvana power chords and hiding behind lank hair, she looked like a sulking grunge-era teenager awkwardly exorcizing her angst in her bedroom.

Her lyrics were the embarrassingly earnest stuff of a teenage diary too. “We’re all gonna die,” she yelled again and again in a song that also saw her spelling out the words L-O-V-E, M-U-SI-C, and T-R-U-C-K. It’s something you either buy completely or find utterly absurd. Most of the half-capacity Knitting Factory crowd was reverential; I did my best to stifle a giggle.

Clap Your Hands Say Yeah and Devotchka play a free show tomorrow night at the Seaport Music Festival at Manhattan’s South Street Seaport.