How to ship CD's

padded envelops. you can also separate cd from jewel case and enclose piece of bubble wrap inside the jewel case

Here's a couple of options to the padded envelope.

http://www.uline.com/BL_1455/Self-Seal-CD-Mailers

http://www.packagingprice.com/forms/product_detail.cfm?categoryID=10173&productID=3001
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The best packagers also placed a thin square of foam inside the case, between the top cover and the CD/SACD so the CD cannot move, and the case top os cushioned from the inside.
Buying one sheet of thin foam and cutting it into 3mm squares would do a lot of mailings.
You can add delivery confirmation to any package for under a buck. USPS online confirmation.

"The best packagers also placed a thin square of foam inside the case"

Yes, I love seeing that thin foam inside the case when I receive an expensive classical CD. It protects the center spindle hole.

My comment should read 3cm centimeter, not 3mm.Sorry