Elvis Presley had that special kind of voice
'I was relieved that all the stuff we'd been feeling for so long found expression in Presley and in rock in general, I was playing his records all the time to friends when they'd come over. I'd say, 'This guy is a great singer' - and they thought this was some kind of inverse snobbery. But it wasn't. Presley had that special kind of voice which makes your heart go out to a singer'.
Leonard Cohen
From Leonard Cohen's interview with Hot Press in 1988 by Joe Jackson (Hot Press: 11 Nov 2016).
'I was a huge fan of Elvis!
'I have plans to sing an Elvis song on stage soon. … 'I was a huge fan of Elvis! I was in town until today and bought a compilation LP of the man. Soon you will hear me sing Don't and Are You Lonesome Tonight - but not at the plate. My voice is too deep. 20,000 cigarettes have led my tone of voice three to four notches down too far.
Leonard Cohen
* While we can't find any recordings of Leonard Cohen singing Don't or Are You Lonesome Tonight, he did cover Can't Help Falling in Love by Elvis Presley. He sings a bit of it, in fact, during this 1988 BBC interview.
From Click Here (BA: March 26, 2012) in Google Translation:
Leonard Cohen singing 'Can't Help Falling In Love; is available on 'The Other Leonard Cohen' Album.
Leonard Cohen's Jukebox
Don't and Are You Lonesome Tonight by Elvis Presley were on Leonard Cohen's Jukebox.