Yews (Taxus species) come immediately to mind, but Myrica (pennsylvanica, cerifera or californica, depending on yor location) would work in a partial shade situation as well and has the benefit of being a native shrub. In your climate, the appropriate species should be very nearly if not fully evergreen.

Yes, wax myrtle (now called Morella cerifera) would be a good choice. Another one to consider is Florida Anise, Illicum floridanum. Both are native plants. American holly (Ilex opaca) might be something to consider as well. Canadian hemlock is very shade tolerant, but the wooly adelgid pest is creating some problems for it.

Good for you on nixing the ligustrum. It is a pest plant in the southeast. Besides, it's nice to pick something different for a change.

From what I've seen and personal experience, no wax myrtle! Limbs are brittle and plant short lived.

You need to tell us where you live first. Not all zone 7s are alike.

Yes, this^, plus, since you indicate a preference for evergreen-how shady is this site? I'd recommend globe arborvitaes-never pruned-as perfect for the specifications you offer, except that if it is 'very' shady, they will not do as I describe. Then too, you're in Z7, I think, and that could be bagworm country. You wouldn't like dealing with that. I'm fortunate to live in a region where-so far-bagworm doesn't survive our winters.

+oM

i doubt that OP will come back... 7 years later.. to give you guys the info you want ...

ken

Uh ya, good point Ken! We do that a lot here!

+om

Surprise, surprise, surprise!! Here I am....Thanks for comments above. I am located in SW Virginia in the Roanoke area. The problem has been pretty much solved since I put up a 6' fence across the back of the yard a couple of years ago, which has given me the privacy I need. There is a large burning bush growing against it, as well as a new Eastern Redbud, and (gasp!) a couple of those evil legustrums, which have yet to cause problems. Also The Elm that Would Not Die, as well as a similarly grim reaper-resistant eleagnus (not sure of spelling) and ditto for a redtip. I am trying to train ivy to grow up the fence but it's pretty resistant (the ivy, not the fence).... So there is my update, and thanks again for your suggestions. I had totally forgotten about posting here!