Cheap Thrills was originally supposed to be "sex, dope, and cheap thrills" but Columbia Records didn't agree; they were nervous about sex and dope, but since cheap thrills didn't threaten them, that became the LP's title. The front cover came about as a result of a meeting between Dave Richards and Rober Crumb, the great Zap Comix cartoonist. One day, Crumb told Richards that he'd love to meet Janis Joplin, and when Janis heard this, she said, "Wow! The 'Keep on Fuckin' guy! I'd love to know him." Dave Getz became enthusiastic, too, and said, "How about getting R. Crumb to do an album cover for us?" Dave Richards promised to discuss it with Crumb.
By this time, Crumb was a minor cult hero. He'd left San Francisco in 1967, when his wife had tried to kill him by dropping thirty sleeping pills into his soup. He ended up in New York, where his off-beat cartoons at last found acceptance in the East Village Other. Returning to San Francisco, he contributed to the first number of Zap Comix and immediately became an underground sensation. When Richards offered him the Cheap Thrills jacket, he said, "Yeah, I'll do your album cover, but the only thing is, when I meet Janis, I want to be able to pinch her tit."
"Why, I don't know about that," Dave said, but several months later, after the album came out, they ran into Crumb at a party. When Dave Richards introduced Janis to Crumb, "he grabbed her tit," says Dave. "She just looked at him and said, 'Oh honey!' and R. Crumb was delighted." The following year, at the opening of the New Comix Show in Berkeley, Janis and Crumb posed for photographers, kissing each other passionately. The woman on the Cheap Thrills jacket is Crumb's idealization of Janis as the ultimate hippie chick, with proud, ripe buttocks and jutting nipples. Crumb also caricatured other members of the band, studying them as they played at a gig one night, and his impressions originally were planned for the back of the album. A high school yearbook layout was to appear on the front, "but the flavor of it wasn't right," Sam recalled. "The back of the album was superb, though, so we just put it in front and it worked."