The problem is with the carriers, but I guess asking Amazon for options never hurts...
USPS "lost" a package from an eBay seller a while back. Their exact words on my third visit to the post office were "Well... It's not lost, we just can't find it right now." Which sounds an awful lot like "lost" to me... I never actually got the package (tracking says it was delivered, though... So it must have been, right?!). Fortunately, the seller shipped a free replacement after I contacted them and explained.
FedEx has left a door tag on my door on numerous occasions saying that they missed me, when they didn't. No joke, I have literally watched the truck pull up, the driver walk to the door and stick a tag on the door. No package in his hands, never even knocked. He seemed shocked when I opened the door and asked if he was planning on actually trying to deliver the package, or just leave a note and run.
Both FedEx and UPS have left "signature required" packages in my driveway more than once. In plain sight, no less.