Released in December 1967, Their Satanic Majesties Request had the working title of Cosmic Christmas, and the Stones imagined it on display in the shops at Christmastime with a 12” x 12” photo of Mick Jagger’s crucified, nude body on the cover. Or so I read in Billboard:

… the Stones originally wanted to call the LP Cosmic Christmas and have its cover featuring Jagger naked and nailed to a cross, Jesus-style. The band’s label, aka the only parent left in the room at this point, nixed it.

A vestige of the concept survives on the finished album in the form of “Cosmic Christmas,” aka “We Wish You a Cosmic Joke,” several seconds of music tacked on to the end of side one after “Sing This All Together (See What Happens).” The unlisted track, an electronic rendition of “We Wish You a Merry Christmas” with psychedelic percussion, is often credited as a Mellotron performance by Bill Wyman, but I believe the few sources that identify the instrument as an oscillator. According to fan lore, you’re supposed to change the speed from 33 to 45 when “Cosmic Christmas” comes on; I’ve embedded a YouTuber’s approximation of the sped-up version below.
 

 
A clever bootlegger pressed “Cosmic Christmas” onto a green vinyl single, mono on one side, stereo on the other, and slipped it into a seven-inch replica of Satanic Majesties’ inner sleeve. A comment on Discogs say this legit-looking “promotional” release came out in ‘78 or ‘79. Could the bootlegger have been trying to steal some Xmas cheer from Keith’s “Run Rudolph Run”? What kind of monster would do that?
 
An amateur comparison of ‘Cosmic Christmas’ at regular and fast speeds:
 

 
‘Sing This All Together (See What Happens)’ in its entirety with ‘Cosmic Christmas’ at the 7:54 mark:
 

Previously on Dangerous Minds:
Lucifer rising: When the Stones were evil