Thank you, everyone for all your nice comments about Fluffy's beauty -- he's a charmer, too!
I've taken a couple more photos to try to show his tail fan. These are taken with my camera phone and cropped, so they're not great, but it is really clear to me what you've been saying about fin damage.
Poor little guy.
I hope I can help him heal. I have a bottle of API Stress Coat. The instructions are vague about how often to use it in cases of damage or disease. Should I use it only when I do a water change or more often? Is there any other product that I should consider to promote fin regrowth?