Tortoise are probably the most important American indie band going who've never sung a word and whose members' faces you wouldn't recognize. Their 20-year career has yielded six studio albums, two collaborative full-lengths, two remix collections, and countless EPs, singles, and compilation contributions. While no outright duds exist in these post-rock icons' catalog, there's plenty of what could be classed as Tortoise-­by-­numbers numbers: ultracompetent, low-­impact output that could waft through postmodernist libraries without causing disruption. For instance, most of 1998's TNT and 2004's It's All Around You abound with expertly played and immaculately produced instrumental rock and ECM-ish jazz that takes "tasteful" restraint to its beigest extremes. Of course, these are exceptions; otherwise I wouldn't be about to summarize—after a strenuous sifting process—this Chicago-based institution's Willis Tower–sized peaks.

One odd thing about Tortoise (John McEntire, John Herndon, Jeff Parker, Dan Bitney, Doug McCombs): Much of their best material doesn't appear on their albums proper, but rather is scattered on limited-edition 7s, 12-inch EPs, and compilations. Therefore, the band's A Lazarus Taxon box set is essential, as it gathers most of Tortoise's many stray cuts in one handy package, while including the group's 1995 remix CD Rhythms, Resolutions, and Clusters and a DVD containing 11 videos).

Enough preamble. Let's examine this Tortoise's most glittering eggs.

"Ry Cooder" (Tortoise, 1994): It starts with a methodical, suspenseful bass/drums/vibes intro dotted with cantankerous, upper-register bass outbursts. Then about two minutes in, the track lifts off, ever so gracefully, with one of the 20th century's most memorable vibraphone motifs; its sangfroid seesaw motion will rivet you within seconds and make you jones to hear it for the rest of your life whenever you crave to put a glide in your stride. Ry Cooder should feel honored.

"Cornpone Brunch" (Tortoise): Tortoise's trademark restraint strains at the seams on this understatedly ebullient tune, which should be used to score a TV segment on an Olympic athlete who overcame great odds to participate in the Games. The song's climax easily earns a gold medal."Spiderwebbed" (Tortoise): A masterpiece of two-bass interplay, "Spiderwebbed" is a subdued, circuitous amble over pastoral vistas. It's like a gentle massage and hypnosis session in one eight-minute track.

"Why We Fight" (A Lazarus Taxon, 2006): This stark, menacing 7-inch from 1995 served as the basis for "Source of Uncertainty" (see below). It's a roiling, hard-punching slab of uncharacteristically pugnacious rock from these unassuming gents.

"Cliff Dweller Society" (A Lazarus Taxon): A 15-minute collage from a 1995 EP, this exhibits more great ideas in one track than most groups do in a career: musique concrète, dub, exotic rhythms, Nino Rota–esque orchestrations, and Miles Davis–­like jazz funk all flow through its mighty river of ideas.

"Gamera" (A Lazarus Taxon): Appearing first on a 1995 EP via Stereolab's Duophonic label, the 12-minute "Gamera" (a tribute to the flying turtle from a Japanese monster flick) starts with John Fahey–esque fingerpicked guitar from erstwhile member Bundy K. Brown. The song proceeds to accelerate with Jaki Liebezeit–ish funky drumming, an epic guitar-feedback symphony, and that subliminally throbbing bass, which recurs throughout Tortoise's career. Brown has been sorely missed.

"The Source of Uncertainty" (A Lazarus Taxon): Originally on Mo' Wax's 1996 Headz 2 comp, this is Tortoise's toughest cut ever. The drums are savage and oddly metered, the vibes manipulated into ominous bell tones, the bass ornery and agitated. The group's usual mild-manneredness subsides, and the change suits them well.

"Restless Waters" (A Lazarus Taxon): A sample of utterly gorgeous pygmy chanting leads into one of Tortoise's most blissed-out creations. Lulling yet spine-tingling waves of keyboards and what sounds like a warped ocarina tranquilly fluctuate, coalescing into an aqueous, Ambien-y reverie. Originally appeared on 1996's The Lounge Ax Defense & Relocation Compact Disc.

"Djed" (Millions Now Living Will Never Die, 1996): Graced by one of Tortoise's most sublime melodies, this 21-minute kaleidoscopic epic could be an American Midwestern interpretation of Kraftwerk's "Autobahn." It has that same easygoing propulsion, expansive melodic beauty, and carefree aura that the German motorik-rollers conveyed in their 1974 hit, but with more postmodern studio trickery, Steve Reich–ian gamelan vibing, and surprising jump cuts.

"TJED" (Remixed, 1998): Drummer/vibraphonist McEntire's remix shaves two-thirds duration off "Djed," condensing it to weirdly FX'd motorik beats and Irmin Schmidt–like keyboard flange. Play this Can-do-spirited jam at your next krautrock-themed party.

"Eros" (Standards, 2001): One of Tortoise's weirdest and best tracks from the '00s, "Eros" sounds like a genuinely fresh update of krautrock's subliminally seductive groove science. The way the guitar, keyboards, vibes, and bass flit, spurt, and sparkle around the beat is like an impressionistic surrealist landscape translated into sound.

"Crest" (It's All Around You, 2004): The peak from the band's second-weakest album, "Crest" soars grandiloquently into a climactic, Hollywood-movie horizon, but somehow maintains its dignity.

"High Class Slim Came Floatin' In" (Beacons of Ancestorship, 2009): A late-career zenith, this eight-­minute stunner combines Terry Riley's mantric, cyclical organ motifs with a flamboyantly muscular analog-­synth riff reminiscent of the best '70s French and Italian prog (think Heldon and Goblin) before shifting into a powerful motorik chug reminiscent of Can's "Mother Sky." (Eye of Boredoms' typically excessive remix is crucial, too.)

Honorable mention: the self-titled 2007 album by Bumps. Under the auspices of Stones Throw Records, Tortoise drummers Bitney, McEntire, and Herndon lay down 23 complexly funky beats (aka bumps, hence the project name) for your sampling pleasure. It's plunderful. recommended