A 3-way light bulb cleverly manages with only two filaments

Why does a 3-way light bulb have only two filaments?  Michele, Someplace, World

A 3-way light bulb has two filaments: one low-power and one high-power. It combines the two to shed light at three levels. The bulb uses just the low-power filament for DIM, just the high-power filament for MEDIUM, and both filaments for BRIGHT.

 A clear 3-way bulb.  Photo courtesy of James D. Hooker, University of Wales.

Three-way bulbs are always made in white finish so its nearly impossible to see the 2 filaments inside, but here's one James Hooker of Lighting Equipment News specially made up a few years ago. You can clearly see the three wires feeding two vertical filaments, one larger than the other, at the center of the bulb.

(Answered June 20, 2001; updated June 2, 2008)