Parcels over ¾-inch thick (or exceed other dimensions required to qualify as a large envelope/flat) but still relatively thin could be packaged in expandable paper envelopes, poly mailers/plastic bags, paper bags or wrap, or even cloth.
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You must package your item properly - unpackaged items can be damaged in transit and damage other items around them. If your parcel is not in a box when your driver arrives to collect, they can refuse to take it.
If the package is not classified as Priority Mail Express™ service (domestic or international), Priority Mail® service, First–Class Package Service™, or an international letter package, it may be opened and its contents examined.