As far as a covering for the top you could use the 2x4 fencing with a layer of chicken fencing over that. If you have two by fours to stabilize it that should make it secure enough up top
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With the electric fences did you have it on a lower voltage so that the chickens could learn not to touch then turn it up?How they get inside? In my case, nothing larger than a mouse ever has. So this is what I did to keep the larger stuff out.
Starts with a tight coop. In my case, a Woods style coop:
View attachment 1157995
Some key features. Note the design incorporates both run and house into one tight structure. Flexible as to ventilation, with two sets of windows that open or close. A Woods coop is essentially a covered run enclosed on three sides. The fourth side, which faces south into the Winter sun, is covered with 1/2" x 1" 16 gauge welded wire. Tough stuff. The rest is 5/8" T111 plywood siding. Only two openings at ground level and those are securely latched. Door is tight. No other way in. This coop is portable, meaning built on two heavy runners. To keep diggers out, there is a 2' wide apron of 1" x 2" welded wire. Shown as installed, before I put the pins in to hold the apron down tight. Within a week or so, grass grew up and covered it and I now mow over it. But still there to keep diggers out. Now and then I see places where it looks like they tried, but never get in.
When varmints show up, and they do, normally, they stand at the opening and stare in:
View attachment 1158008
But no joy. Can't dig in, can't break in and can't reach in, so tough luck to them.
That protects the birds during the day, or during several days in a row if I'm not around to let them out. They have food, water and room to play inside the coop. Then, during the day, they are contained within, and protected by, a 4 wire electric fence.
View attachment 1158009
It may not look effective, but it is. Brutally hot and painful to anything who might want to test it.
This flock is going on 18 months and no losses to date from any predators......and they are around. Foxes, coyotes, possums, skunks, dogs and cats and who knows what else.
It can be done.
With the electric fences did you have it on a lower voltage so that the chickens could learn not to touch then turn it up?
How big is that electric run you have and may I ask about how much $$$ it cost?