Consider Clap Your Hands Say Yeah the Little Brooklyn Band That Could: They made it, and they did it all with one of the dumbest names in indie rock.

But, more important than overcoming their self-consciously unpunctuated debacle of a name, the band set a new standard for outsider success stories. Back in 2005, Clap Your Hands Say Yeah proved it was possible to garner a large and devoted following, plenty of fawning press and an array of auspicious comparisons — all without the backing of a label. Their Internet-driven success was a testament to the growing power of music blogs and online commentators — and, yes, to the quality of their self-titled debut album.

“Some Loud Thunder,” their second effort, is a satisfying follow-up to the first. But if it seems unlikely to win over new fans, perhaps that’s to be expected — after all, the still-unsigned band doesn’t appear interested in reaching out with any kind of formal publicity machine. Instead, they’re content to produce a few excellent songs. At that task, they succeed admirably.

“Satan Said Dance,” a twitchy, compulsively danceable track, is the album’s highlight. Like many of the songs on “Thunder,” “Satan” takes a while to settle into itself, taking its time to arrive at a pulsing rhythm. It spends almost a minute squeaking the musical pieces into place, even scrambling through a clatter of piano, before becoming utterly irresistible. The build is effective and persists throughout the song’s five-and-half minutes. The only element that nags is the chorus’s irritating call and response: The crowd of bright voices threatens to push a song about disco hell into too-cuteness. Singer Alec Ounsworth’s endless intonation of the word “Satan” gets under your skin, and every time the crowd pipes up with the inevitable, chipper “…said dance!” it’s a disappointment.

Ounsworth has a voice like a saw. It’s rough and wobbly, and it tends to work away at phrases for a while before splitting them into something interesting. Although Ounsworth’s style has been compared to that of Neutral Milk Hotel musician Jeff Mangum, the two vocal instruments seem to be put to different use. Ounsworth doesn’t have Mangum’s piercing, pained quality — he seems somehow more diffuse, more inclined to meander. In doing so, he stumbles upon some intriguing moments: On the album’s second track, “Emily Jean Stock,” he flirts with something a little like Dan Bejar’s meowing Bowie-isms. While not always successful, moments like these keep the listener engaged.

It’s hard to see how “Some Loud Thunder” could disappoint any of the band’s devotees: It picks up the catchiness of the debut, but also pushes into more meditative territory. But it doesn’t do anything to overshadow the most exciting thing about Clap Your Hands’s success: the story of the unsigned band that made good on the big bad Internet.