If you court obscurity long enough, it becomes a kind of fame. This is the lesson of Mayo Thompson, who made a rare appearance with his band, the Red Krayola, Wednesday night at the Knitting Factory.

The Red Krayola began in the psychedelic glut of the late 1960s and were outliers even then. Whereas the mood and moment drove many respectable groups to grow out their mop tops and shrug off traditional song structures, it was just barely weird enough to accommodate the strangeness of the Red Krayola.

The band’s 1967 debut, “Parables of Arable Land,” put out on the same cult International Artists label as better-known psych pioneers 13th Floor Elevator, alternated down-the-rabbit-hole pop tunes with clangorous instrumental “free form freak-outs” that made Captain Beefheart sound like the Beatles. The intended follow-up, “Coconut Hotel,” was rejected for being weirder still. Instead, the band released the tamer “God Bless the Red Krayola and All Who Sail With Them,” which prefigures the blank wit of Jonathan Richman.

If it had ended there, the Red Krayola would be a prime candidate for rediscovery by the psychier side of the freak folk movement (Vashti Bunyan, Gary Higgins). But Mr. Thompson has never been one to rest on his lack-of-laurels. Since reforming the band in the mid-1970s, he has put out a steady stream of unlistened-to albums (most recently on tolerant Chicago indie Drag City) that have subverted every subversive genre from post-punk to no wave, lo-fi, free jazz, and noise rock.

Mr. Thompson’s itinerant talents were on display Wednesday night. He started with a lounge number that could have come from Paul Schaeffer on the “Late Show With David Letterman” (a comparison suggested by keyboardist Stephen Prina’s mild resemblence to the bald-headed bandleader). That was followed by a haunted country number reminiscent of Neil Young that started out quoting from “Will the Circle Be Unbroken,” but quickly spun off into something about “dialectical imperialism,” “new product realism,” and “electrical surrealism.”

Mr. Thompson is a deconstructionist at heart. He is a bottomless well of melodies, and his band is good enough to carry them off in whatever style he chooses. But he is only interested in the negative aspects of songs. His most hummable riffs and rockin’ moments are all setups: He weaves rugs only to pull them out from under you.

The Wednesday night show felt at times like a music randomizer. One minute Mr. Thompson and his band are playing a weighty Primus riff, then they’re noodling and plucking like expert sound effects men scoring a radio play as Mr. Thompson croaks some unintelligible narrative into the mic. Just as suddenly, they’re rocking again, playing a faintly familiar blues riff like the best damn bar band you’ve ever seen.

The only constant was Mr. Thompson’s miserable vocals. He rarely bothered with a vocal line, preferring instead to bounce around within a song, seeing where his deflections might lead. Watching him, I found myself thinking of the hapless contestants in the early running of American Idol that they invite on just so the judges can mock them — only here, Mr. Thompson is the one doing the mocking.

But as the set wore on, something strange happened: Mr. Thompson won me over without my knowing it. Every time I thought I’d start making my way to the exit, I was stopped in my tracks by something surreal or sublime. Often both.

Drag City labelmates White Magic seemed like a natural fit to open for Red Krayola. They’re one of New York’s better young psychedelic bands, playing tuneful plodding songs thickened with little ragtime piano parts and Mira Billotte’s delirious vocals. (Think Badly Drawn Boy playing in an opium den.) Unfortunately, they suffered by comparison. Everything they did sounded too carefully off-key and off-kilter. It wasn’t weird enough to interest or offend.