And, by the way, I fixed it. I was using an old version of Image Handler that I'd downloaded back in March. I went back to the folder that I'd uploaded, and every file associated with Image Handler got deleted, and those modified by Image Handler got replaced (there were only two or three that were modified). Perhaps the newer version, posted by the illustrious Mr. Ladywig.com, is more solid than the one I downloaded. I won't be finding out out of general principle.