I guess our yard is a good size ... we have 1/3 acre ... and we love it ... but when the tree service cut down our maple, he said "These trees shouldn't be grown in small yards like yours." It kind of intimidated us to planting anything but "small" trees. Nevertheless, as I have been aptly reminded by many comments here, and I thank you for them, our yard really isn't that tiny, and there is a lot we can do. I just remembered that my neighbor is growing a white pine at the back of their property, so I don't know what I am worrying about. We do have a large white pine at the far back corner of our property, so there is shade there, but not until the afternoon. We love that tree even though it's huge (80' I'd guess). The rest of the backyard is a blank canvas. Thanks for all the suggestions ... we will look around more & consider all our choices & not be too hasty. The thermometer said 98 today ... this shouldn't be until July !

Where in SoCalifornia? Give a town, please. Big difference between Zone 9 USDA or Zone 9 Sunset. Can you plant ON the slope, or is it outside your property? How far is it between the house and the slope? You don't want a tree that eats the house just to hide the slope. Cottonwood is a definite hazard - they get big, then fall over or send huge limbs flying in storms. Consider a mix of medium size vertical-growing shrubs with small-to medium vertical-growing trees along the back of the yard. If I knew where you lived I could be more specific.

One of the problems of the area that jumps out at me is all the blank wall space on your neighbor's house. It's a primary view that a tree would take care of. On your own house facing the street is some of the same, so another tree is in order. Insofar as giving a sense of privacy while not enclosing, I would suggest a spaced series of small, multi-trunk trees -- like crape myrtle -- that insulate from view anyone who is a distance away on the street while it allows you to see what's close. If you spend some time developing a good trunk arrangement, you'll get more screening (like a visual filter) out of the trees as the trunks develop. To develop the privacy even more and get a sense of protection, place a bed of groundcover below the multi-trunk trees. It should a height that allow your view to easily continue above them. You'll be viewing below the tree canopy and in order to do that, it should start at about 9' or 10' off of the ground. (I pollard crapes to 10' every year.)

Take this diagram as a very general idea about where you might consider placing trees. It doesn't mean you can place trees at any and all locations along the line, but that it's a starting place to evaluate tree placement. Often one tries to keep some centrally located open lawn space, but this is not a hard rule. Much depends on your specific needs and desires. You would want to take into consideration the specific tree and its size and habit, other competing features in the yard, and architectural features of the house, etc. If there are any very small trees (in the 10' to 15' range) they might go closer to the building in front of blank walls. (For these type trees I usually use multi-trunk trees that are more commonly thought of as large shrubs.)