Doctor, Doctor, give me the news

Moon Martin - Bad Case of Loving You (Doctor, Doctor)
Here's another I just found out about recently. Famously covered by Robert Palmer, the original was written and performed by Moon Martin from his 1978 album Shots From a Cold Nightmare.

Ciccone Youth - Addicted to Love [originally by Robert Palmer]
A side project of Sonic Youth, Ciccone Youth released The Whitey Album in 1988 with this Robert Palmer cover, which was sung by Kim Gordon and recorded at a karaoke booth in a mall.