There's no doubt Dylan's voice deteriorated in the late 80s, but I have to agree Tim that with these more recent Sinatra/American Standard cuts, his voice is sounding a lot better - more like an old crooner, than a Tom Waits' screecher. There's 3 albums in the series (the last being a triple album, so effectively that's 5 albums of material), but I would cut to the chase and only listen to the following 9 tracks:
The Night We Called It A Day
Some Enchanted Evening
Full Moon and Empty Arms
That Lucky Old Sun
All the Way
Skylark
Melancholy Mood
Once Upon a Time
My One and Only Love
There's a nice version of Dylan performing 'The Night We Called It A Day' on the final Letterman show....
https://www.youtube.com/watch?v=BoJhS6JPcjA