Problem with CD Baby cds

I have this problem a lot with older CD's and my Marantz; but I can always download them to WAV and put them on the playlist.

Hope that helps.

Thank you all for your suggestions.  Ripping the files and then burning them to a CD-R does the trick.

BUT.....  I'm the guy that likes to cruise through my cds.  I like to read liner notes.  And I sort of think that when buying a "cd" it ought to play on a decent transport.

Oh well...

I have exactly the same problem: some CDs just won't play. CDR copy plays fine, CDRW(!!) copy plays fine which means that the lens is clean (i opened the player and cleaned it with Zeiss lens cleaner anyway). 
Total mystery to me! But at least it is not CD Baby fault, at least not in my case
My only idea was that it is somehow related to copy-protection. Yesterday I got (I think) proof that it is not copy-protection either. 

We may never find what causes the problem, but since misery loves company, it's nice to know that we have plenty company; just kidding.

@orpheus10 it does sound comforting that I am not the only one! Any search for Wadia players returns a lot of misery! I am not alone!!! ;-(
I still want to get to the bottom of these unplayable CDs, so when my son was visiting us over the weekend I put him to work! Using his Linux running laptop he discovered that all of my unplayable CDs (total of two!) have more than 800MB of info written onto them! Using Nero I can make a copy of these discs on 800MB/70min CD-R (and they play fine) but if you want to get a bit-to-bit perfect copy you just can not. I will buy CD-R blanks for 900MB for his next visit to see what happens. Will report then. 
Why would Naim CDS3, CDX, and all of my Discmans would play these discs and Wadia won't?  Maybe folks at Wadia are not as smart as I want to believe!?! Wadia does sound magical, and beats Ayre, Krell and McIntosh on SACDs (but thats a common knowledge),... canNot beat CDS3 on CDs (but who can?!!?)