My overall plan is to shade the center of the backyard with a couple of trees. From working out in the yard, it seemed clear that the East and West parts of the backyard, with plenty of shade from various trees, does fairly well, even in the heat of the summer. As the sun moves from East in the morning to West in the evening, both ends of the yard get at least some direct sun, but not for the whole day. The West part of the yard gets the morning sun, up until just after noon, when the large oak tree at the West end of the yard shades it. The East part of the yard gets afternoon sun.
But the center of the yard seems to be direct sun all day. So if we plant a couple of trees to the left and right of the center, it should, eventually, shade all of the yard, at least part of the day. Since we want the sun in the winter, we want a deciduous tree, and for variety (we have mostly oaks), we decided on pecan trees. If the pecan trees give off nuts, that's good too -- both for us and for the neighborhood squirrels.
Since the East half of the yard is done, it could take a tree. To reserve space, we have put a volunteer oak tree where the pecan will go (and a stick where the other goes). Since we don't have the West part of the yard done yet, nor the center, we can't put the second tree in yet. But we can put in the first tree.
Today, we went to Berdoll Pecan Farm and Nursery and bought a tree. We have been buying our pecans from them -- in bulk, cracked but not shelled -- and figure that they have good pecans, so they must have good trees. We bought a medium size Pawnee tree. $49.99 (plus tax). It is 53 inches tall.
We planted it in the spot reserved for it in the East part of the yard. The instructions from Berdoll say to water it every day for the next 30 days, so every day in April.
The volunteer tree that was filling in for it was moved over to where the next tree should go. It will probably be a couple of years before this gets dug up and we can put another pecan tree in it's place.
The information sheet from Berdoll suggests that it will be 4 to 6 years before we get any nuts from this tree. So around 2020.
Update: It appears, in May 2018, that we will have nuts on the tree this year.
Update: There were a dozen or more very nice looking plump pecans developing on the tree, but suddenly one early September morning, they were all gone. Just disappeared. Nothing on the ground; nothing left on the tree. (5 Sept 2018).