Hi. You might want to look at the following:
1. Little leaf ash (fraxinus greggi). It can grow to 15 ft. high and about 8 feet wide. It is an ideal tree for the Phoenix area, not too large, is drought-tolerant, and should fit into your back yard without any problem. It is deciduous, but, in Phoenix, it shouldn't be too much of a problem.
Three other trees you might consider are:
1. Catclaw acacia (acacia gregii) which grows to 18 feet with a width span of 15 feet. It is also deciduous, but great for Phoenix.
2. Blue Palo Verde (Ceridium x Parkinsonia), which grows to 20 X 20.
3. Desert Willow (Chilopsis linarus), 20 X 15. This is not a true willow, although it looks like one. It is more closely related to the western catalpa.
For a list of trees that are great for your area, you might try the following website:
http://www.epwu.org/conservation/plants.html

Here is a link that might be useful: Desert Gardens

I have a tree that I think fits the bill but I don't know the name of it. It's leaves look like a Ficus tree but it gets spikes of tiny white flowers. The flowers are really not very ornamental, more a fuzzy look than true flowers. Bees love them as do hummingbirds. We have a repeat nester in ours for the last 3 years. The Tree is 4 years old and about 7-8 feet tall and about 7 foot across base. It does take prunning well, just need to get my hubby on the ladder to get the top of it.
We water it once a week in the summer, deep, and everyother week in the winter. It does get a little water greedy when it blooms so I tend to trim about half of them off since they start to weigh down the branches too much anyway. I think it might have Japanese in its name, sorry not much help. If your interested I could take a pic and posted it. It sheds very little leaves, the only "shedding" time is from the blooms that turn into small pods. Since I trim most of them off I don't notice clean up. It's not a huge tree but it does shade my pool room very well from the setting sun.

Pithecellobium flexicaule (Texas Ebony) is a beautiful evergreen tree for the low desert. Many great examples in Phoenix. Check them out at the Desert Botanical Gardens.Enjoy! dl

I vote for the desert willow...beautiful, large trumpet shaped flowers in either white, white edged in pink, or white edged in purple... Several together are great as a screen and open, dappled shade. Twisting stems, usually multi-trunked, but can be trained to one trunk if you want.