I am trying to mail greeting cards that have small clay tile (1"x1")
affixed to the front.  I spoke with the post master of the local post
office.  He recommended that I place a piece of corrugated cardboard
between the tile and envelope (that made the problem worse).  I tried
using harder clay and that worked a little better but still didn't
solve the problem.  I placed bubble wrap between the tile and envelope
and that still gave me about a 25% breakage.  I don't want to use a
cardboard envelope because it will increase the cost of mailing.  The
cards are 4 1/4 x 5 1/2.  We don't care if the envelope costs a little
more but we want to keep the mailing fee at 37 cents.  How can we mail
the card without them breaking and keep the price of mailing from
going up?

Hi clayhands,

The problem is, your tiles are being sent through the sorting machines
and are getting squashed. Lots of padding would probably be the
easiest solution (not just one or two sheets of bubble wrap but you
would have to wrap the card at least twice around to be effective) but
would make your cards too thick to send for 37 cents. To keep your
letters thin enough to pass for the .37 rate but at the same time
offer enough protection for the tiles,  you'll need to inset the tiles
inside little frames, making them untouchable - experiment with
various material and thicknesses to get just the right combination.

Start by using 1/8" cardboard or styrofoam sheets.  
Cut two squares,  2" x 2" each.
Cut a 1" x 1" hole in the center of each square. Depending on how many
you need to make, this can be done using an exacto knife or handmade
hole punch. The idea is to make the hole just the right size so that
it can be pressed on to make a snug fit.
Fit one frame on each side of the tile. If the tile isn't exposed on
the back of the card, you'll have to glue or tape the frame to the
card on the back.

The size restraints make this a challenging project, but framing the
object is the proper way to prepare a delicate item for shipping.
Other options, such as rigid envelopes, are costly and still don't
eliminate the problem of pressure being put on the tiles. Again,
bubble wrap will work if enough layers are applied.

Example of rigid envelopes:

STAYFLATS  MAILERS - Kraft
Fiberboard shipping envelopes  6 x 8: 100/$24.55
http://www.riversidepapercompany.com/main_files/mailers/mailer_Stay_K.html

I hope this works without too much trouble! If you have any questions
or if this isn't a workable solution for you, please post a
clarification request *before* closing/rating my answer and I'll be
happy to reply.

Thank you,
hummer

Search Strategy:
I have alot of experience with shipping and used my personal knowledge
for this question.