It looks like all the aerators at Home Depot are - at smallest - 15/16" in diameter. My faucet apparently requires one a good deal smaller than that. I haven't measured, though. I'll have to do that.

I also haven't gotten around to taking the thing off. I'll have to wait until I can get in there around the disassembled toilet. Turns out that one was running too, needed a new overflow pipe, and wasn't a good toilet anyway. We're just going to replace it.