The American singer in question is Janis Joplin.
Proof you ask?:
- "Though he has lately told interviewers that he regrets having let slip that this song was written to Janis Joplin, it's a detail he has regularly announced during concerts in recent years." - The Book of Lists: The 90s edition, page 88.
- A firsthand noder report from Albert Herring - Leonard Cohen "explicitly said it was Joplin on stage at the Hammersmith Odeon, 1978 or so."