In my former job, the USPS was the bane of my existence. It now just seriously annoys the heck out of me. I did, however, learn some "useful" stuff…
http://pe.usps.gov — this is the ultra geeky, official USPS "professional" site — it differs from the regular USPS site in that it has alllll their arcane rulings and all kinds of templates, calculators, etc. If you use it, you will probably end up knowing more than your average postal clerk.
The two issues I noticed most people complained about above are the surcharge for square, and the surcharge for "bumpy" stuff. There’s this weird formula to calculate an "aspect ratio" that’ll tell you if you have to pay what I call the "funny shape surcharge," which is basically if your envelope isn’t "normal envelope shaped" — including squares. I have no idea why they hate squares, but they do.
The other thing they hate is not being able to send your mail through their mail-eating machines. Should you give them something that denies these beasts potential food, they complain…and charge you more. That includes bumpy stuff AND things they determine "too rigid" — so, if you send anything like a pen, or a pair of chopsticks, or a popsicle stick, you have to pay that surcharge too. Also, clear plastic envelopes; they charge extra for those too. (Vellum/glassine are, I think, still OK, but those mylar ones, or clear plastic, not so good.)
Also, there’s a class of service called "First Class Flats." It’s different from "First Class Cards & Letters" which is what most mail in envelopes we’re used to falls into. If you move up to the "Flats" designation, your piece can be a bit bigger in dimension, and may be OK w/ some of the characteristics that are no-no’s for "Letters." Of course, it costs more. It IS, however, LESS than "First Class Parcels" (box-ish things) or Priority mail.
If in doubt, print out the DMM (Domestic Mail Manual – it’s on the site I referenced above) page that seems to support your case, and take it to your postal clerk to prove why you should/shouldn’t get the rate you think you should.