Even though they were well on their way to being one of the most important bands of 1969 and 1970 (and, you know, American rock music in general), nobody remembers that Creedence Clearwater Revival played at Woodstock.

Seriously, they totally did.

Nobody remembers they played there because A) CCR weren’t in the movie and B) John Fogerty, the band’s singer/songwriter/leader/legendary control enthusiast, was rumored to have been displeased with the band’s performance and never bothered to capitalize on the recording. (He also famously complained that the previous act, the Grateful Dead, had put everyone to sleep. He really liked disliking things.)

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The first reason is factually correct. The second, if true, is a shame.

As revealed in the recording of CCR's performance released earlier this month, “Live at Woodstock” (Craft Recordings), they played a terrific set, beautifully recorded. Even when Doug Clifford speeds things up a bit at the expense of the groove (as 24-year-old drummers have done since the beginning of time), it’s vivid, crunchy stuff.

But one can see why Fogerty might have declined further exploitation, and that reason is timing. To listen to the Woodstock set is to hear an absence of the band's biggest songs. What, no “Down on the Corner”? No “Who’ll Stop the Rain”? Why not play the hits?

Here is the thing to remember about CCR. They released one album in 1968, THREE in 1969 and TWO in 1970. (Their finale, 1972’s “Mardi Gras,” is, to put it charitably, a bummer.)

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Let me repeat that: From May 1968 to November 1970, CCR put out SIX albums in about 29 months. Nine of their singles (out of 11 released) in that time hit the top 10, most of them with B-sides that were easily as good as the A-sides. CCR were the Fernando Valenzuela of '60s rock acts: astonishing numbers in a very short amount of time.

“Green River,” their second album of 1969, had only been out TWO WEEKS when Woodstock took place. This wasn’t a supergroup making its debut a la Crosby, Stills and Nash or a thunder god making iconic music (hello, Jimi). This was a band that was just starting an incredible run playing one of many, many, MANY shows.

So, their Woodstock set is filled with deepish cuts, such as “Commotion” and “Bootleg,” and a cover of Ray Charles’ “The Night Time is the Right Time,” as well as tight readings of “Born on the Bayou,” “Green River,” “Proud Mary” and the still-perfect “Bad Moon Rising.” The band cranks through nine tunes in 35 minutes, which was about how their albums played out; those tended to run eight to 10 songs in about half an hour.

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Après Ray, le déluge. The album closes with two near-11-minute workouts: “Keep on Chooglin’” and “Suzie Q.” In keeping with the band's Berkeley-plus-New Orleans vibe, CCR's idea of a jam was a near hypnotic focus on a basic riff with solos that owe as much to hooch as acid.

“Keep on Chooglin’” sounds particularly visionary, a “Sister Ray” for flannel shirt set-welding kraut rock simplicity with a one-chord vamp, while “Suzie Q” blasts off and feeds back into territory that folks decades later would identify with stoner rock or Seattle mud.

Welcome back to the Woodstock story, guys. We had no idea how much we missed you.