The first nest was made of rubber bands and the first of two pigeon eggs lies within.  Pigeons lay two eggs per "clutch" and incubate them for several weeks.  To prevent Hedwig from delpeting her supplies of calcium and other nutrients we feed her dove food and pigeon grain along with as much pigeon grit mixture (contains crushed oyster shell, mineral salt mixture, charcoal, and other good things) as she will eat. 
We also replace her own eggs with wooden eggs which fool her into sitting on them, so that she does not continue laying continuously.
After all, these unfertilized eggs are not going to hatch despite Hedwig's maternal determination!
(Dog & Cat fur Hat at right... made with donated hair from the three critters below)