First, I checked the spare and all the tools in the back (the spare had 10 pounds of air instead of 60, so this was not a wasted effort). Everything seemed secure, so I removed the spare tire and all the tire tools. Still rattled. I removed every removable compartment in the back. Still rattled. I checked the security of the 12 volt battery--it was tight. I put padding between the plastic covers that hide the rear seat belts. Still rattled. I folded down the seats. Still rattled. I tried padding on the rubber supports for the hatch lid. Still rattled.
I got under the car and looked for something loose--couldn't see anything wrong. I stuck my hand up inside the bumper area and found a square (aluminum?) bar. I could move that about 1/8 of an inch. That made quite a bit of noise. This bar runs the width of the car (the plastic rear bumper that you see must be primarily decorative); I suspect this bar is what absorbs any blow harsher than a shopping cart. This cross bar attaches (somehow) to the frame on the left and right sides of the car. On the passenger side, there was about 1/8 inch of play. Why there is play or how to properly tighten the bar are questions for someone with a lift (not me).
I took one side of Velcro tape and removed the backing. I stuck this to the offending pieces of metal (the Velcro tape is very sticky) and it stopped the movement and noise. Sugru would probably work as well.
Whenever I take the car to my independent mechanic, I'll get him to address the reason and proper fix for the movement.