I found some really beautiful little handblown modern stemless cordial glasses in a fabulous shade of ruby red, but they are either dirty or etched or something...I've tried pretty much all of our usual standbys to get rid of a white line area just under the rim of the glass, but nothing works. I remember reading about some dishwasher additive that made that particular kind of white line go away, but I don't want to put these in the dishwasher.

Does anyone know of any miracle chemical to make these lines go away? Thanks. If all else fails, I'll smash them for mosaics, but I really do like them in this form and would love to keep them this way.