A little known fact is that if you ship via the Postal service using either Express or Priority Mail, the intercity movement will almost always be by either FedEx or UPS, with the USPS delivering "the last mile." This won't be true if you're talking about intra-state mail but anything going any amount of distance (i.e., by plane) will be handled by one of the two big commercial companies.
Problem with this, if you read the fine print, is the liability limit when you use this method is only $100. Presumably the coins you're submitting likely have a total value of more than that, if they're worth submitting.
Update Got an E-mail back from ANACS, and yes the address I posted is a valid physical address for FedEx/UPS/hand delivery/etc. However, next month they are moving, so if you're submitting anything by this method be sure to call them first (1-800-888-1861) before submitting to get their new address. If you're submitting by USPS, their PO box address will remain the same. (Another option is to hand submit them to ANACS at any coin show they're attending, a schedule of which is at their website.)
Well in that case why not cut out the middle man lol... and for 1 day delivery, UPS and FedEx are both actually cheaper than USPS's express mail. Sometimes even cheaper than Priority Mail, depending on the weight of the package.
