Here’s the thing about Deerhoof: they’re the kind of band that will name an album “Friend Opportunity.” But they’re also the kind of band that will fill the opening notes of that album with as much aggression as they can muster.

Deerhoof is a band about contradictions, and this is their central one. If it were their only one, though, they wouldn’t be nearly as interesting as they actually are. They’re cute but loud! But they’re more. Rather than just sharing a winking one-note joke with their audience, they write songs like an army of sharp little shape-shifters. On “Friend Opportunity,” the band finds myriad ways to keep their audience both off-balance and enthralled.

Take “The Galaxist,” a standout. The song opens with an inviting ripple of guitar — and it’s nice, but it’s boring. Something’s amiss. Thirty seconds in? An enormous pang of dissonance, and some drums. But this isn’t just musical attention-deficit disorder. That rippling guitar line comes back, only amplified, multiplied, until it’s stopped being easily melodic and has become eccentric and spacey. And after a few listens, it begins to seem unsettling — a little anxious, a little too quick — even in its original incarnation. And then, of course, there are the hiccups of total silence that punctuate the middle of the song.

Deerhoof is constantly pulling the rug out from under your feet. There’s a marching band in “+81,” but it sticks around for less than ten seconds at a time. “Whither the Invisible Birds?” darts back and forth between a sweeping, melodramatic synthesizer and what sounds like an impatient ten-year-old at a piano lesson, deliberately plunking out notes. This sort of abrupt shift happens on the scale of the album as well as within individual songs. The second-to-last track, “Look Away” clocks in at almost 12 minutes, unfolding slowly in spite of the steady fire of two-to-three minute songs that makes up the rest of the album.

“Friend Opportunity” builds on the strengths of “The Runners Four,” Deerhoof’s 2005 release, heightening both the drama and the pop appeal found on the previous album. The distinctive presence of singer Satomi Matsuzaki remains a constant. Her breathy, heavily accented vocals essentially serve as an instrument: most often, instead of conveying meaning, they’re just providing another sound. This is not a complaint — in fact, it’s an engaging part of the texture of Deerhoof’s music. When you pick up a phrase here or there — “Hey, it sounded like she said ‘pinky toe!’” — it feels like some kind of charming coincidence, like spotting shapes in clouds. Of course, as much as this makes the lyrics secondary, they’re still a snappy part of what Deerhoof does, and when they’re made more central — as on “Matchbook Seeks Maniac” — it is to good effect.

If there is an important overriding contradiction to be found on “Friend Opportunity,” it’s not the cute-but-loud one that Deerhoof flaunts most obviously. It’s the band’s seamless combination of bouncing accessibility and difficulty — a related but subtler paradox. That difficulty feels at times like petulance, but, weirdly, that’s part what makes it enjoyable. Deerhoof teases, alternately lingering on and pulling back from what the listener wants. And, remarkably, the album holds together. This is music cut with pinking shears: it’s jagged, but it’s whole.