The bottom "nipple" unscrews easily. There are three screws holding the glass to the metal part where the glass goes. But if I unscrew the screws holding the glass part on (at the top of the glass part) it's still held in by the bottom piece. If I try to unscrew the bottom piece, after removing the easily removable nipple, the whole electrical part with the bulbs twists inside the glass, so nothing is actually unscrewing.
This is in a tight area that requires a ladder, increasing my lamp-based frustrations.