Under The Covers: Other Artists Covering Beatles Songs: ‘Dear Prudence’- Siouxsie And The Banshees. This is one of my favorite ever Beatles covers. John Lennon wrote this while they were in India with the Maharishi. Influenced by Mia Farrow’s sister who became obsessed with the medication to the point where she was secluding herself from everyone else. One of the best songs on The White Album- the cover is just as great.