"I don't know your circumstances - maybe you have not noticed an update to CC and could be using who-knows-what version.
So are you using v5.29?"
I did an update and ran the cleaner the same day that I posted so yes it is the most recent version.
""..for as long as I have had Edge" - well, that could be since last Friday."
It has been longer than that. Over a year at the least, maybe longer.
"Help is best when facts are involved. :)"
Everything I said was fact, nothing I said was untrue.
"I assume Edge - or any MS related program - is NOT running when you run CC?
Other MS related software could include Skype, Live Mail, etc."
I'm pretty sure it wasn't, but I will double check to make sure next time.
"In CC, do you have any cookies to keep listed?"
Only the default ones, I didn't add any.
"What about within Edge itself, have you tried deleting the history there, then going back to the CC method after that? (just to see if it gets you over this hump)"
I haven't. That certainly could do the trick but doesn't explain why the program isn't doing it.
"One other question - do you have Cortana running?"
Yes.
"If Cortana is running then URL's from Edge can/will be saved to the Microsoft cloud, where CCleaner can't get to them."
I did not know this.