A member was interested in buying a small part from me and we agreed on sending it in a regular mailing envelope since it was cheap and used. I sandwiched it between two thin pieces of cardboard just to be safe and had it taken to the post office ready to mail.
I was told it would be $6.55 which is the rate of a parcel of the same weight, and I didn't even bother sending it since it wasn't paid for yet anyway.
I called a closer local post office and told them about the option on the USPS website that's $1.30 to ship a rigid envelope internationally, but I was told that once a rigid abject is enclosed, it becomes parcel rate.

So why is there even an option if it's not available? There's a $.20 charge for being rigid compared to a regular envelope. Taken from the USPS website:
First Class Mail International (letter)
A nonmachinable surcharge is applied to a First-Class Mail International letter, if it has one or more of the following characteristics:
Has an aspect ratio (length divided by height) of less than 1.3 or more than 2.5.
Is polybagged, polywrapped, or enclosed in any plastic material.
Has clasps, strings, buttons, or similar closure devices.
Contains items such as pens, pencils, or loose keys or coins that cause the thickness of the mailpiece to be uneven.
Is too rigid (does not bend easily when subjected to a transport belt tension of 40 pounds around an 11-inch diameter turn).
Is more than 4-1/4 inches high or 6 inches long and less than 0.009 inch thick.
Has a delivery address parallel to the shorter dimension of the mailpiece.
For self-mailers with a folded edge perpendicular to the address, the piece is not secured according to DMM 201.
For booklet-type pieces, the bound edge (spine) is the shorter dimension of the piece or is at the top, regardless of the use of tabs, wafer seals, or other fasteners.
http://ircalc.usps.com/LetterProperties.aspx?country=10013&m=1&p=0&o=1