This has been discussed in many forums, especially the trees forum, how to get privacy in the shade. You may want to do a search there.

If it is really shady, nothing will grow very quickly. Hemlocks can get quite large, but also can be pruned to stay as a hedge. But given long enough, anything will keep growing taller.

Why a tree instead of shrubs?

How about arborvitae or yew? Yew is slow growing but does well in a lot of shade. Vining euonymous could be trained up a chain link fince to provide narrow evergreen privacy.

Here is a link that might be useful: privacy trees in NY

Thanks for the link! I didn't find my answer there but helps me learn about other options. My height requirement is a real drag. I don't need a tree, a tall shrub is what I want, I guess. 20 feet because of the electric wires. The reason I mentioned 'tree' is because those neighbor kids (and their parents!) lean out of their second story windows and watch my every move. Slightly unnerving to look up and see that I have an audience. I was thinking a servicberry, which would grow to just the right height, in 15 years or so! A holly too would be managable. As for the arborvitae idea, I had considered it, even though I'm not a fan of it's looks, but since the October storm I am seeing all of these tall slanting specimens that were weighted down by that snow. The site is not full shade, it gets morning sun. I would like a hemlock. I don't need complete privacy, just a distraction from the side of my neighbors house! Alas. I'll keep reading the forum and hope I can come up with a good solution. Thanks for your suggestions!

Sappy ~
Have you considered the Japanese Tree Lilac, Red Buckeye, Various Magnolias, Japanese Maples, Fringe Tree, Paw Paw, Chinese Dogwood, Cornelian Cherry Dogwood. I have Mimosa (Albizia julibrissin) seedlings from a local source. I also acquired Mimosa 'Summer Chocolate' seed that have not sprouted.
These will remain about the 20' mark that you mentioned.
I grow all of these,plus large, unusual trees in my yard in Hamburg.
Sources ~
Johnson Nursery, East Aurora, NY
Perry' s Nursery, West Seneca,NY
Dan Majeski Nursery, West Seneca, NY
Menne Nursery, Amherst, NYI
Plus I use mail order for hard to find plants and start many from seed...

Hope this helps...
~ Gerry

You might consider a pussy willow. In 8 years, mine has gotten about 10-15' tall, and about 8' wide, from a very small whip. You can prune out larger branches to keep the height down.