I'm looking for a tree to provide some shade on our patio. The problem is there is only 5 1/2' distance between the concrete patio and our wooden fence so want something where the roots will grow down and not out. I'd prefer to have an un-messy tree since it will eventually shade our patio. a Full-top tree would be great and probably provide the best shade eventually. I'd like to plant this tree before June, we live in Orange County, CA.(Southern CA). I'm not opposed to spend a bit more to start with a little bigger tree.

Right now I'm clueless and tree less and appreciate any suggestions.