I don't put fencing materials over the top of the garden - yet anyway. The fencing keeps the rabbits out, and not the young ones or the chipmunks. To keep the small rabbits out I have, in the past, put a layer of hardware cloth around the bottom of the chickenwire fence. I have a friend that uses old screen windows to do this.
What I found that works really well for young tender plants is to use coffee cans, juice cans, milk jugs, and 2 gallon plastic buckets, all with the bottoms cut out as a barrier to critters. I put them around the plants until they are big enough that they are critter proof. Rabbits will eat a young squash or cucumber plant but when it's about 12 inches they don't bother them anymore. I then remove the coffee can from the plant. Mind you these plants are STILL inside of a fenced in garden space but a rabbit will jump a 30 inch fence, John and I have watched them do this, to get to young tender plants.
The cans etc., also protect young plants from wind damage and make them easy to cover in the event of a hard frost or freeze.
For the crows what I've used in the past are cds on strings etc. and strips of mylar from mylar balloons. I live in Iowa so wind is a constant here, most critters don't like the movement and tend to keep their distance. The crows seem to be enamored with snapping off my young tomato, pepper and squash plants. So the cans, I use the smaller coffee or juice cans, prevent them from getting close enough to do this. They also like digging up my onion sets! Hardware cloth tent prevents this from happening - but isn't chipmunk (ground squirrel) proof.
Daring squirrels - I have dogs so the squirrels are not as daring as they'd like to be, and they know I've no problems with taking them out, squirrel tastes really good with mashed potatoes and gravy btw! Fry it up like chicken. Critters seem to pick up on human attitudes ;-)
As for possums, they don't seem to navigate the fencing well, and I don't have skunks here - praise the Lord for that one! That could be a real nightmare with the weimeraner that loves to chase everything - she's not all that bright.
I'll go take pics of my garden and post them in a bit.