At USDA/NASS we use FedEx all the time for packages and envelopes, especially for 'priority' deliveries. It’s no secret that the USPS is suffering. Instead of 'outsourcing' shipping AND bailing out the USPS why not keep all mail originating from federal offices in the federal system and use the USPS? The USPS offers the exact same services as FedEX and since it is in the federal system, in theory, our federally protected data would be more secure. The money for mailing things is going to go somewhere, it might as well be used to fund the USPS. Two birds with one stone: our office mail gets delivered and the USPS gets the assistance it is going to get anyway.
In response to comments: Let's not forget about Express Mail Guaranteed which is faster than Priority Mail. Also, comments suggest, the USPS should have a preferred provider status and/or bulk cost break contracts with federal government.