Thanks everyone. I did some searching on the web. It looks like it might be
aiptasia, as several of you suggested. One site claims that various fish will
eat these, including the Copperband suggested by Mislav. Copperbands and Racoons
are supposed to be the best. Queen angels also alledgedly like them, so I'm
going to get one of those.

There's also a nudibranch that eats them, but when they run out of aiptasia,
they starve. I'm not going to chance that.

George Patterson
We don't stop playing because we grow old. We grow old because we stop
playing.