Just realized this morning
 

...in that weird half-waking state, that the verses of "Back To Her Man" are the same melody as "Is That It, My Friend?".

Probably one of the deeper subliminal reasons I never loved the former song. Still adore the earlier one, though, and hope this doesn't mean he'll ever stop playing it.

the lyrics for Is that It my Friend are 324135908435 times better

Indeed. There's certainly that aspect too.

Is That It My Friend is one of my favorites. I don’t mind the lyrics to back to her man but I think he introduces it with the Cohen back story, which makes the lyrics seem creepy. And, something about the chorus sounds funeral “marchy” (perhaps intentionally?). He or someone here said something about Back To Her Man being too much of a “Cohen” homage. Do you know to which Cohen song they are referring?

I'm not sure it's any one Cohen song (although the droning funereal march rhythm could certainly be likened to many Cohen classics like "Suzanne") in the same way that "Baby Sister" is a blatant rip-off of "Famous Blue Raincoat".

The weird irony of that story Damo tells about Cohen is something I related in one of my very first concert posts here back in 2004: "...There was one other funny thing I forgot to mention. As we were driving home we were still excitedly talking about how nice it was to talk to Damo and what a great guy he is. Heidi's listening to "O" on the headphones and suddenly she says almost to herself "He's so hot!" I laughed and said "Did you just say 'He's so hot'?" She said "No." I said "it's OK if you did. I'm not jealous I just thought it was really funny the way you said it -almost like when no one else was around or something." She said "I don't think I'd have said something like that -out loud". She still says she didn't but I think she did."

So, Mr. Rice: "Physician, heal thyself!"

to me it doesn't sound like any Cohen song in particular