Pigeons on birth control?

What next? Hollywood pigeons are being put on birth control to stem their population. The birth control agent will be put in rooftop feeders and will interfere with egg development. I assume only pigeons, starlings, and house sparrows feed from these feeders and no native birds would ever try to eat from them. I also assume that this agent can't be passed to a predator like say a Peregrine Falcon who dines on pigeons. Let's hope my assumptions are true.