Thanks for all the tips, John. I'm working on the "power problems" theory: that it didn't get set in the charger properly, or the contacts were dirty; after that, it may be time for new rechargeable batteries.

It has magically fixed itself for the moment, while I wandered around trying to find out what happened to the original mouse that came with this Mac (the cordless is a Logitech).

~ Becky in Tucson