I have flight netting on top of my Run with a six foot tall fence. I live by a River, have a pond and woods so I have many predators. My run has been up a year and so far nothing has gotten in (knock on wood) But I do lock up my chickens before night fall in their coop. So I am assuming a predator is not going to waste time and energy to get into a fence that no food source is in at the time. Most wild predators roam at Dusk, Dawn and at night. Not that a wild predator might not get at your coop in the day time. I would do what you feel safe with and at what cost you can afford. My run is huge! It would have cost me hundreds of dollars to build a run with wire on top. I also have 4 Roosters in my flock that may help with smaller predators.