For the stuff you don't want the post office to touch / screw up / fail to deliver / whatever -- pay the $4 / item prime rate for one day delivery. No post office involved then.

My only complaint with amazon using usps for the last-mile delivery (fedex smart-post, whatever ups's equivalent is) is that being just outside a good-sized city, fedex/ups will get it to their facility in a day or two, and then the post office will take another full week to move the package 5 miles.