If you check the USPS website you will find that there is such a category called RIGID.

Click Mail and Ship.
Then click Calculate a Price.
Enter the appropriate information and click on Calculate price based on Size and Shape.
Enter weight and click on LETTER, not package.
Now click on Content is RIGID.
You will now get all the options for mailing a RIGID LETTER. Scroll down to First Class Letter. Basically the cost is at the First Class rate plus a surcharge of $.15. 1oz would be $.55+.15=$.70, 2oz would be $.70+.15=$.85 and so on.

I have been attaching my own postage, marking the front and back of the envelope with DO NOT BEND in red ink and dropping these into a mailbox or giving them to my mailman for the last couple months. So far, none have been returned to me.