Terra Incognita was produced by Mars Volta's Omar Rodriguez-Lopez. Lewis told Q magazine February 2010: "I personally believe Omar Rodriguez-Lopez to be the Jimi Hendrix of our time and I risked humiliation by asking this genius to help bring my ideas to fruition in a way that was more like the weird visions in my head."
The Terra Incognita album cover shows Lewis yanking the leash of a huge bull. She told Q magazine that she got the idea for it after hearing Rodriguez-Lopez play this song. Said Lewis: "That bull came to me in a vision through Omar's guitar. He was playing a riff on 'Female Persecution,' a song about witches being burned at the stake. The riff told me a story about a bull. At that moment I knew I must have a bull on a leash. It cannot be photoshop-ed! The bull in the vision represented my power and whether it can be tamed. And, of course, I live in the town where movies get made so you can rent a bull! There's a bull-renting service in the directory! He's a movie bull called Willie. He was docile but I was scared of him. In fact, I cried when he came out of the crate because he was just so beautiful. Every time he put his head down to eat something I thought he was going to charge and gore me to death, which would have been quite an album cover all on its own."