MEW ARE without a doubt among the most underappreciated rock bands of the decade we’re exiting. Not that they’ve received as much as a single bad review: almost no smart listener fails to rate them as highly as they deserve, but plenty of smart listeners who should be worshipers have never heard them at all. (Some are frightened away by the artwork, no doubt.) It’s a shame, since Mew are at very least as important as the fawned-over Sigur Rós, who incidentally feature a lead singer who is Mew vocalist Jonas Bjerre’s almost-exact sound-alike. Bjerre’s voice is the vastly more versatile of the two, dipping from angelic highs (no falsetto, by the way) to dusky baritone lulls. And while his band’s unusual, imaginative music shares with Sigur Rós an aura of otherwordly seduction, Mew’s thrashing, hazy heaviness has more in common with My Bloody Valentine, Swervedriver, and other thunderously loud members of the shoegaze hall of fame.

Until Sony picked them up for 2003’s Frengers, Mew was a highly-influential local act, consistently inspiring contemporaries in the Copenhagen rock scene and winning regional “band of the year” awards. Mostly a sampling of tracks from their late-90’s Danish releases, Frengers registered as a blip in the American consciousness, getting less notice than one would expect for how startling yet imminently listenable it is. One American reviewer aptly described it as “all hooks, all the time, with little of the verse-chorus-verse predictability that can water down a pop song’s impact, but also with no trace of pretentiousness or preciousness.” Frengers sinks its fangs with a swelling opener and never lets go. Pace varies, instruments play on top of one another in different time signatures, songs stop as soon as they’ve begun. But Bjerre’s hallowed voice binds it all together, sailing, floating, swooping over the top of the roaring mixes below. Every single track is haunting.

If there is a better way to meet a new face on the world rock scene, I don’t know what it is, and Mew seem to count on listeners having been along for that introductory joyride. Their second global release, And the Glass Handed Kites, was more ambitious, somehow holding even more jutting edges and strange juxtapositions together into a cohesive, paranoid whole. It’s a thrilling concept record with constant spine-tingling tension between innocence and malice. But there were still plenty of sugary choruses to help things along: the rollicking “Apocalypso” and the lush, sky-scraping “Zookeeper’s Boy.” Amazingly, these unabashedly whimsical songs, soaked in synthesizer and laced with inscrutable lyrics, required no suspension of disbelief—not even a little.

The new record’s official title—No More Stories are Told Today/I’m Sorry They Washed Away/No More Stories the World is Grey/I’m Tired Let’s Wash Away—seems to test our willingness to accept Mew’s persistent reaches into the absurd. Recorded at a hideout in Brooklyn, it feels instantly more wordly and effort-laden, more workaholic New York and less romantic Scandinavia. The song-shapes are deconstructed even further than on Glass Handed Kites, where they were essentially all movements of one grand piece, but they’re put back together with great care—sometimes too much care. There are more complex tricks than ever—starting with the backward-playing opener “New Terrain”—that obviously were a labor to create, and are sometimes a labor to appreciate. Only the rotating, danceable “Repeaterbeater” begs for endless repetition, and it’s barely two minutes long. But if you’re willing to study the carefully calculated experimental formulas, you don’t care quite so much that Mew doesn’t have their usual clear-cut solution in mind. No More Stories tries to be about the elegance of the reasoning, and a significant chunk of its running time is thoughtful if not very entertaining.

A clangy distorted guitar (think “Circuitry of the Wolf”) does some mind-bending borrowing and carrying throughout “Introducing Palace Players,” one of the several multi-movement tracks that unfold with long, patience-rewarding arcs. (Another is “Cartoons and Macramé Wounds,” a seven-minute opus that can play at different moments—much like the epic Frengers closer “Comforting Sounds”—as a slow-burning winner or a droll procession that no one should be asked to sit through.) The breezy “Hawaii” finds traditional Polynesian instruments performing Mew’s typical manipulations of rhythm, forcing competing layers of percussion together until they explode into soaring, high-register choruses. It sounds a bit hokey, an affliction from which Mew have never suffered before, but I’ll give them credit for the track’s sheer unusual-ness and overall listenability.

Hard-rocking pop songs (“Snow Brigade,” “SheSpider”) are such a Mew specialty that a record without them would be truly difficult to accept. No More Stories only has one: “Vaccine,” which still sounds lighter and happier than most Mew songs—it’s full of bubbling vibes, plunky piano, and moments without a hint of bass—and doesn’t quite match any of them. In fact, this record regularly falls prey to its attempts at casual positivity. The boppy, hand-clappy “Tricks of the Trade” doesn’t do much to improve on the screechy Scandinavian trip-hop formula, as it has neither hooks nor wizardry and suffers from an unvaried mid-tempo trot. A similar lethargy overwhelms “Silas the Magic Car,” which sounds like both a campfire singalong and a b-side (neither being a compliment). Let’s face it: Mew are most themselves when they’re waking up from snowy nightmares, not when they’re drinking mimosas by the beach in Hawaii.

For all its stretching of the bounds of time signature and key, No More Stories is an uneven effort that takes too much time to get into and doesn’t offer enough reward for the effort it asks of us. There are some things only Mew can do, and they clearly worked their asses off to bring it as hard as they always do. But when we’ve heard how wondrous and magical they can be, a plodding record like this feels something like a step down.