Trees or evergreens with dark leaves make spaces look smaller, but you can plant trees in a small garden that don't enclose you by planting one with soft pale green or yellow/golden leaves. The Acer Palmatum "Sango-Kaku" is ideal for a small garden. It has yellow/golden leave in the summer and in autumn they turn apricot yellow. Even after 10 years, the tree is only 8ft in height and 6 ft wide. Eventual height and width is 20 foot and 16 foot, but its a relatively slow grower and you can keep it in check by pruning it back. Its probably more of a large shrub then a tree and is ideal for a small garden because it grows upright.
Another good way of screening is bamboo - but it does need containing to stop it creeping around. Very easy to stop bamboo creeping - simply get a large plastic trug in a dark colour and cut the bottom of it off and then bury the trug (without bottom) in the ground, and then plant the bamboo in it. Leave the trug sides about 2 inches above the soil, so the bamboo can't creep sideways or over it. There are two forms of bamboo - clumping and non-clumping. Go for a clumping one as they tend to keep themselves together better. Go for a bamboo with light green/yellow/golden leaves and stems.
You could increase the height of your fence by topping it with trellis. People complain about high fences, but don't seem to mind trellis, because it doesn't block out light and views completely. Once installed, run climbers up the fence and encourage it along the trellis. Before you know it, you've got a comptely covered treliis, which if you choose the right combination of plants (Honeysuckle, Clematis, Winter Jasmie, etc, you could have colour and privacy all the way thru' the year.
Remember that the fence to the right side of the house, as you look out the back door can often belong to your neighbour, so seek their permission before attaching something to it. You can look at the deeds for the house and the side of the boundary with the inward facing T on it, is your responsibility, in which case, is your fence to do as you see fit. Note that not all deeds have this T shown.