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You mean songs that were released, but never appeared on Greatest Hits albums?
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Great observation!!  ::)

Those songs may have been good to you or I, Doc, but they may not have charted.  Or they may be lesser hits than the ones on the albums.  :)  Maybe if you went to a country site (like Country Weekly) they'd be able to help you with this question. :)

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Anne Murray had a hit in the 80s called "That's Not The Way It's Supposed To Be" (from her album "A Little Good News"), but it's not included on any of her greatest hits albums. Barry Manilow had a hit in the 80s called "Some Kind Of Friend", but it's not included on his greatest hits album (which is called something like "The Greatest Hits And Then Some"). What's up with that?!
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Those were good songs, man! It does suck when they cheat you out of the one song on their Greatest hit compilations. Like, they released a Sheena Easton one and it didn't include the "The Lover In Me" track. Duran Duran didn't have "New Moon On Monday" on their "Decade" one either!!!  >:(
I sure don't get it.

Quoting:
Anne Murray had a hit in the 80s called "That's Not The Way It's Supposed To Be" (from her album "A Little Good News"), but it's not included on any of her greatest hits albums. End Quote

Not really sure on this one, it never charted in the Hot 100. Maybe it wasn't a single? ???

Quoting:Barry Manilow had a hit in the 80s called "Some Kind Of Friend", but it's not included on his greatest hits album (which is called something like "The Greatest Hits And Then Some"). What's up with that?!End Quote

This song can be found on at least 3 of Manilows Greatest Hits albums. Greatest Hits, Vol. 1 from 78, Twenty Classic Hits from 85, and Greatest Hits: The Platinum Collection from 94.

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It does suck when they cheat you out of the one song on their Greatest hit compilations.
I sure don't get it.
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Some other omissions from greatest hits albums:

"The Cream of Clapton" does not have "Lay Down Sally" on it
"Vital Idol" does not have either "Rebel Yell" or "Eyes without a Face" on it (although Billy Idol's newest greatest hits CD does have those two songs on it, plus a live version of "Rebel Yell"!)
The Police's "Every Breath You Take--The Singles" has an entirely different version of "Don't Stand So Close to Me" (called "Don't Stand So Close to Me '86") on it (but if you want the original version, get "Every Breath You Take--The Classics")

And the worst of all--a CD by country singer Ronnie Milsap called "The Essential Ronnie Milsap" does not have any of his 1970's hits on it!  The liner notes don't even mention all the great country hits he had in the 1970's!  Duh!  It's as like he never recorded anything in the 1970's!  It's like his recording career began in the 1980's!  Which is not true!