My reasoning with probably 99.99% of Cohen covers is that the performer puts far too much of themselves into the song instead of letting his stark words speak for themselves. One case in point, in a myriad of cases, was the butchering of, 'Hallelujah,' where a whole succession of singers thought they could do better than Cohen and turned a gem into tarnished glass. Sorry, NYCBlue, Cave's version also falls into this trap.
However Cave's 2015 restrained rendition in London I believe is much closer to the song's essence.
https://youtu.be/w5AjWTOTMg0
Janileigh Cohen, clearly allows the song to sing to us by not getting in it's way.
https://youtu.be/OsU_nYDF4TM
And of course, the Cohen original live:
https://youtu.be/xxaOcHcrd8k
StT.
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