We had the same concern, so what we did was fairly inventive, I think. We built coop-knox, per many of the recommendations on this site. Then, we built a very heavily constructed run that is 6X8 (we have 5 hens) and permanently and securely attached to the coop. It's covered with hardware cloth and while I'm not going to say it's impenetrable, but I would be very surprised if a predator ever made its way in. Our dog hasn't let anything hang around long enough to find a weakness, if there is one.
Outside of that area, we have a much larger (~2500sf) run that is fenced, but not covered. The ladies can scoot back into the secured run if they feel threatened and we feel comfortable knowing that once we've closed the door they are as safe as we can make them.
We like the way it has worked out because the smaller run is easily maintained and accessed. At the same time, it's big enough for them to hang out in the morning until we go feed/water and let them free range.