I've always used a small amount of ammonia in warm water. Soaked.

It has worked fine on a few pieces over a hundred years old, but I don't know about other pieces.

Thanks. I'll try that.

I post about this stuff nearly once a day. I should buy stock, I guess! I use it for hard water stains on everything from shower appliances, both metal look plastic and real metal, tile and grout and the glass shelf on my shower set up. I've recommended it to people for cleaning glass shower doors. Someone recently was thrilled with the results, maybe on the bath forum?

My window cleaner uses it on windows (he didn't learn about it from me, but his company uses it) to remove rain spots from windows. Just yesterday, I used it to get the haze out of the bottom pot of my pyrex double boiler (where the water sits). It never looked clean because of the haze. It took all the haze off and it looks brand new. You can get it more affordably at Ace Hardware and maybe a free sample. I think the company will send a free sample, too. I've only used what comes in a tub, so can't say if the bottle is the same stuff or not.

You could try glass cooktop cleaner/polish. It's a liquid and shouldn't scratch. Magic Erasers will scratch glass. Ceramabryte is a good brand and Scotchbrite has one now that I also like.

Vinegar if the haze/residue is from hard water scale (calcium chloride.) I would NOT use the eraser stuff, that's pumice and can scratch.

The haze is hard water deposits which are a pain. I read you can use commercial products on crystal so if you have something on hand like Lime A-way, you can try a little spot to see if it works. Or use what Oly suggested, and I think I might get some of that!

We have hard water and vinegar and all that other homemade stuff does nothing.

I've used the stuff Oly posted about after getting a sample at Ace but mine came in a bottle -- bought at Ace. We used that stuff to polish hard water spots off the bathroom fixtures and tub drain in my sister's former house before she moved. I thought we were going to have two replace them, but with a little time and patience -- we didn't! If vinegar doesn't do it, I try that. Those are both apparently acidic -- ammonia would be alkaline and might take off deposits acid cleaners don't. Just don't combine them and wash off any reside before switching.