Thanks everyone for their advice and experiences with ick. All of my fish have recovered from the ick, and all but one loach is perfectly back to normal. (I believe the loach is having non-ick realted issues).
What temperature is your tank if you have tetras, loaches and goldfish in it? Raising the temperature is often recommended for treating ich (I do it) but that would pose problems for the goldfish (which shouldn't be mixed with tropicals, anyway).