Shana Levy has lots of famous friends. She used to be the keyboard player for LA indie rockers Irving, she plied her trade on Rilo Kiley’s debut album, and her songs have been publicly endorsed by the likes of Courtney Love and Rodney Bingenheimer. The Flaming Lips love her so much they’ve been playing her unfinished demos as their between-set music for years. And on top of that, for The Chaos in Order, her debut full-length under the Let’s Go Sailing moniker, she’s got Weezer’s producer, Modest Mouse’s engineer and collaborators who’ve worked with Elliott Smith and Jenny Lewis. A list like that is enough to make anyone jealous—even a little resentful. Toss in the child-friendly band name and some refrigerator-worthy album art that walks a very fine line between delightfully twee and annoyingly cutesy, and there’s every reason for a cynical 21st century rock critic to hate her before the music’s even started playing.

But then the music does start playing, and you forget about all that. As it turns out, The Chaos in Order is an excellent debut album of gentle, bittersweet pop tunes. Levy mixes bright melodies and catchy hooks with melancholy strings and softly strummed acoustic guitars for a sound that is at times reminiscent of Aimee Mann (on “All I Want From You Is Love”) or Mates of State (on the opener, “Sideways”), but is always sweet, heartfelt and understated. Sure, those are ridiculously common traits in the modern world of indie-pop, but Levy manages to separate herself from the rest of the pack. A lot of that has to do with her lyrics. Plenty of bands with melodies this good fall flat when it comes to the actual words they’re singing, seeming to toss in their lyrics almost as an afterthought. But Levy has obviously given them some real consideration. The Chaos in Order is littered with clever lyrical snippets, like the first few lines of “Heart Condition” (“This heart condition that you have / Is not all it’s cracked up to be / It’s not bringing you / The attention that you think / It ought to be”), and the opening verse of “Icicles” (“All the icicles are falling down / Like tiny little daggers in the ground / I better run for cover / Or they’ll soon be / Sticking in the softest spots / Inside of me”). They help give a depth and meaning to the songs, something similar songs by other bands are lacking.

That’s not to say the album is without its drawbacks. Her ballads are a bit of a weak spot; slower songs like “Too Many Stars” and “This Rope is Long” feel more like filler than worthy compliments to her stronger, upbeat material. And there definitely is a fine line between twee and annoying. Too much of anything this sweet runs the risk of becoming irritating after a while—no matter how much you love it. Even given the melancholy undercurrents, 40 minutes of Levy’s tunes will be more than enough for some; The Chaos in Order is not a record for the cynical or the easily annoyed. Those clever lyrics sometimes seem too precious, and her vocals—which she recorded herself at home—occasionally come across as breathy and strained, something that could quickly get under your skin if you are already having a grumpy day.

But why worry too much about grumpy people? They’ve already got punk rock and emo and grunge. For those of us who like a little cheeriness mixed in with our gloom—and whose record collections are no strangers to the schoolyard charm of bands like Belle & Sebastian and the Boy Least Likely To—Let’s Go Sailing will have no trouble fitting right in.

• Multiple songs MySpace