Several mailing envelopes and boxes are designed specifically for sending CDs and DVDs through the mail safely. The type of mailer you need depends on a few factors, namely whether you're sending the jewel case or DVD case and how much you're looking to spend on postage.
Bubble Wrap Envelopes
Bubble wrap envelopes are mailing envelopes lined with bubble wrap cushioning to protect the mailer's envelope. Bubble wrap envelopes can be found relatively inexpensively at most office supply stores like Staples and Office Depot and large retailers like Walmart. These envelopes are typically large enough to accommodate one or two CD jewel cases or a DVD case, depending on the envelope's size.
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Cardboard mailers are similar to the paper sleeves some CDs come in, but are made of stiff cardboard for extra protection. The slim size of cardboard mailers make them better suited when you're sending the disc only, as most can't accommodate jewel cases or DVD cases. These can also be found at many office supply stores and may result in slightly lower postage due to their lighter weight compared to bubble wrap envelopes.
Priority Mail DVD Boxes
The United States Postal Service sells boxes specifically designed for sending one or two CD jewel cases or DVD cases safely in the mail. These Priority Mail DVD boxes are very slim and don't offer much room for packing materials like bubble wrap, but they're made of sturdy cardboard and should protect CDs packed in jewel cases. Postage on Priority Mail DVD boxes is prepaid when you buy the box, as long as the package weighs less than four pounds. International versions are also available if you're sending CDs to someone in another country.
When packing CDs for mailing in a box or envelope, bubble wrap is definitely your friend -- especially if there's a chance the disc will move around in the box. Cut a pair of squares out of cardboard to sandwich the CD between, and then wrap it in bubble wrap. If you're sending several loose discs, stack them with a square of cardboard between each disc before wrapping the stack in bubble wrap. Pack the box or envelope with shredded paper, packing peanuts or more bubble wrap in order to keep the discs from moving around in the box.