With Coachella 2012 a mere month out, I can’t be the only one wondering: How many of the groups slated for this first-ever double-weekend bash will go all-out and deliver distinctly different sets?

A few of the shows are sure to be somewhat standardized (after more than a decade away, Dr. Dre isn’t likely to switch it up much within a week’s time), but one performance that surely won’t be a repeat is Radiohead‘s.

Case in point: a rare double dose of the legendary British quintet in Austin, Texas, over two consecutive nights (Tuesday and Wednesday) just before the launch of next week’s South by Southwest music conference. The first night was the band’s debut appearance on Austin City Limits, America’s longest-running music television program (launched by PBS in 1976), held at the practically brand-new and super intimate Moody Theater (capacity: 1,700 capacity). The second gig, held at the massive Frank Erwin Center, was (correct me if I’m wrong) Radiohead’s first proper Austin show since the mid-to-late ’90s, circa The Bends and OK Computer.

Both shows were clearly special for their own reasons. But a huge part of what left me reeling after the two-night stand was the prospect of what might be different yet equally mind-blowing about Radiohead’s imminent Coachella turns, based on changes in those sets and others on this tour thus far.

For the television taping on Tuesday, new material dominated, whether off The King of Limbs or in arrangements born from post-album sessions. The show opened with three of ’em: “Bloom,” “Little by Little” and “The Daily Mail,” the latter a piano jam crescendo that surfaced on The King of Limbs – From the Basement, issued on DVD last December.

The relatively tiny studio audience (which included one of Austin’s newest resident musicians, Robert Plant) was also treated to a kinetic rendition of “Staircase” (another from that DVD), a trip-hop-inspired new cut called “Identikit” and the down-tempo, hauntingly jazzy “Skirting on the Surface,” a tune that frontman Thom Yorke presented in stripped-down demo form during “solo” gigs with Atoms for Peace in 2010.

While the Erwin Center show the next night began with that same trio of songs — as well as choice Hail to the Thief cuts “Myxomatois,” “The Gloaming” and “There, There” — it did not include “Staircase” or “Skirting on the Surface,” nor did it feature “The Amazing Sounds of Orgy,” a rarely performed and entrancing B-side (for “Pyramid Song”) that the band debuted live the night before the taping in Dallas. Hearing that dark, notably swing-influenced composition (on which Yorke plays bass) in such a small space was a priceless experience, especially given how infrequently it might crop up again.

Likewise, bassist Colin Greenwood and drummer Phil Selway’s rhythm section (enhanced by guest drummer Clive Deamer, borrowed from Portishead) has never resonated as crisply on euphoric In Rainbows selections like “Reckoner” and ‘Weird Fishes/Arpeggi” as they did for this ACL show. Ed O’Brien and Jonny Greenwood’s maddening guitar licks on the encore-closing “Paranoid Android,” meanwhile, rang out at penetrating, nearly death-metal volume.

Still, there were a slew of equally irreplaceable moments the next night, too, each bolstered not by the naked-eye-intimacy of the preceding show but rather the arena-size production, made up of four enormous layers of textured screens, with 12 suspended, square-shaped mobiles displaying vignettes of the band members throughout the show.

Most memorable in that batch: “Kid A,” so much more powerful than usual thanks to Deamer’s second layer of frenzied yet proficient beating; the succeeding “The National Anthem,” a tune that, even without Deamer (who stepped offstage briefly here and at other junctures), culminated in a most intense electro-jazz-rock and sample-heavy freak-out; and a spellbinding, softly-lit arrangement of “Nude.”

Also unique and affecting from the second night: the bulk of both encores. The first began with “Separator,” a showcase of Radiohead’s most finessed and emotionally precise guitar loops, followed by “These Are My Twisted Words,” a TKOL-era single focused very little on lyrics, instead emphasizing intricate layers of fretwork from Yorke, O’Brien and Jonny Greenwood and emanating a phaser-heavy, Eastern-twanged sci-fi feel.

After that spacey exploration, the band pulled out its biggest guns of the evening: the decidedly earthshaking rocker “Bodysnatchers” and then “Everything in Its Right Place,” a cacophony of ambient purple lights and patterns permeated by the musicians’ most esoteric sample sequences.

Encore two commenced in mellow form, just Yorke and Jonny returning at first to execute the loop-laden “Give Up the Ghost,” a calming segue to the build-up of “You and Whose Army?” — the only track chosen from Amnesiac over the course of both nights. The show concluded with an undeniably spirited run-through of “Paranoid Android,” this time even more potent due to the apocalyptic black-and-white-to-tv-test-card light patterns enshrouding the group as Yorke spun and thrashed about, acoustic guitar in hand, like a berserk imp.

For all the differences between Tuesday and Wednesday’s performances, however, there were admittedly more similarities. That seemed unavoidable, though, given the obvious focus on new material and the fact that the first show, being a television taping, was abbreviated relative to Radiohead’s typical output. For Coachella, the band will undoubtedly play full sets, and not one day but a full week apart. That’s ample time for these musical sorcerers to rehearse and craft myriad pleasing variations. Fingers crossed for more live debuts and deep cuts.

Setlist: Radiohead at the Moody Theatre (ACL Live), Austin, Texas, March 6, 2012

Main set: Bloom / Little by Little / The Daily Mail / Myxomatosis (Judge, Jury and Executioner) / Morning Mr. Magpie / The Gloaming (Softly Open Our Mouths in the Cold) / The Amazing Sounds of Orgy / Staircase / Reckoner / Weird Fishes/Arpeggi / Identikit / Lotus Flower / There, There (The Boney King of Nowhere) / Feral / Idioteque

Encore: Skirting on the Surface / Paranoid Android

Setlist: Radiohead at the Frank Erwin Center, Austin, Texas, March 7, 2012

Main set: Bloom / Little by Little / The Daily Mail / Morning Mr. Magpie / Myxomatosis (Judge, Jury and Executioner) / The Gloaming (Softly Open Our Mouths in the Cold) / Kid A / The National Anthem / Reckoner / Weird Fishes/Arpeggi / Nude / Identikit / Lotus Flower / There, There (The Boney King of Nowhere) / Idioteque

First encore: Separator / These Are My Twisted Words / Bodysnatchers / Everything in Its Right Place

Second encore: Give Up the Ghost / You and Whose Army? / Paranoid Android

Photos also by David Hall, for the Register.