cleaming fabric lampshades

I have 3 lampshades that are really nice. I like the shape, size and color (ivory). But they are very dirty. I expect some of the dirt comes from my DH's cigarette smoking as it is that gummy brownish color. I tried a foam carpet cleaner but at first it just made it worse. On the second try it cleaned some areas.
My mother in law's neighbor swore she put hers in the bathtub and gave them a good scrubbing. But I think mine have areas that are glued on so I expect that would come off.
Any suggestions, please?