From the San Diego Natural History Museum Bird FAQs:

Mockingbirds are keeping me awake at night. How do I make them shut up?
Sorry, there is nothing to be done short of leveling your neighborhood of all trees and shrubs. If the habitat is suitable, mockingbirds will use it. And the landscaping typical of residential neighborhoods in southern California is ideal for mockingbirds. The Museum cannot advise you to violate the Migratory Bird Treaty Act, which protects all native birds of North America. According to the Act, all native birds are “migratory birds,” whether they migrate or not.

Motherfuckers.