If you don't want to let your cats run free, don't keep cats.

As for cats killing birds, well yes, they do. Obviously. But cats are almost certainly not the cause of decline of bird numbers, ever. Do read this, which is from the RSPB website, and stop worrying about your cat killing birds.
   http://www.rspb.org.uk/advice/gardening/unwantedvisitors/cats/birddeclines.aspx

I've had cats for most of my long life, and I can see all too plainly when they've had birds. It just isn't that often. My current cat, which we've had for almost three years, has left us evidence of just three bird kills, and I promise you that I never turn a blind eye. On the other hand he's had dozens of mice and rabbits, for which I am most grateful, and I haven't seen a rat round here since we've had him.