Davy,
You don't tell us what zone you are in, but if you are in zone 9 or under, SKy pencil Holly might do the trick.
They can be shaped too.
You also dont tell us if it is full sun, or part sun, I think the Sky pencil will grow in both.

how will you maintain the 3 feet... at 20 feet high???? 8 foot ladder isnt going to work ...

and do understand.. plants dont stop at some given size ... with the height you want.. with the 3 foot width .. you will be signing up for a lifetime of pruning ...

i might be thinking more along the lines of a pergola ... see link

you are in a plant box.. i suggest.. you step out of it.. to consider all kinds of alternatives ...

i really dont see a plant remedy here ...

ken

Here is a link that might be useful: link

Post pics of the problem area with a description of what you need privacy from or for.

A plant that grows 20 feet tall and stays only 3 feet wide at the base? I can't think of anything except Giant Bamboo and you don't want that.

Here's the sun/shade side it's probably more like 3-4' of space. Trying to keep privacy from neighbor.

Here's the sun side it starts off at about 5' then tapers off at 3' of space. Trying to keep privacy from neighbor.

We are not interested in bamboo because of its invasiveness, not even anything like cypress because it's not beautiful in such a tight area plus it catches spiders and dust.

I love English laurel, Monterey bay Eugenia and pittosporum (needle looking leafs - can't find the name).

Someone suggested Afrocarpus gracilor :) thanks to all those who replied I Appreciate your response!!

None of those will fit in that width. Not so much the root system but the actual spread of the shrub. With the exception of very narrow growing choices - like columnar conifers and the Sky Pencil holly (which is very unlikely to reach 20'...more like 10' max) - shrubs will rapidly develop widths that will overhang and encroach on that already narrow side yard. Frequent pruning or shearing will be a heavy requirement.

Believe it or not, bamboo is the ideal screening plant for this situation. It will achieve the desired height far more rapidly than any tree or shrub and in a confined area like this built up planter, is perfectly safely contained. And there are also many types of clumping bamboo that could be used that pose NO invasive issue, confined or not.