The original inspiration was a romantic encounter that producer David A. Stewart of Eurythmics had with Stevie Nicks of Fleetwood Mac. On The Howard Stern Show, Stewart explained that the title's phrase was actually uttered by Nicks. She had broken up with Eagles guitarist Joe Walsh the night before, and invited Stewart to her place for a party after an early Eurythmics show in Los Angeles. Stewart did not know who she was at the time, but went anyway. When the partygoers all disappeared to a bathroom for a couple of hours to snort cocaine, he decided to go upstairs to bed. He woke up at 5am to find Nicks in his room trying on Victorian clothing and described the entire scenario as very much reminiscent of Alice in Wonderland. Later that morning, she told Walsh, "Don't come around here no more."

The music video is themed around Alice in Wonderland and was directed by Jeff Stein. Dave Stewart appears as the caterpillar at the beginning, sitting on a mushroom with a hookah water pipe while playing a sitar. Petty appears in the video dressed as The Mad Hatter, and actress Wish Foley played Alice. At the end of the video, Alice, who has been turned into a cake, is eaten by Petty and even friends of her own, after which she wakes up from her dream.

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