This time it didn't work. No error messages in the restore, but when I tried to access the site (front-end or back-end), the browser didn't go to the site, but gave me a SAVE dialog (to download some php file that is not in my base directory).
Based on error messages in Akeeba, I had recently upgraded PHP to 5.5, but I set it back to 5.4 to see if this was the problem, and it wasn't.
I do local backups on the test site (Akeeba 4.1.2), and I'm able to restore them.