Try a mastic (aka evergreen pistache). They don't get too big (15-25' tall) but they will get quite dense. And they are evergreen, so they'll block the mess year-round.

Ours is doing very well here in Tucson, we only water it about once a month and it's happy and green. It's also a very clean tree.

For the lowest water use, choose a type of tree that is native to your area that fits the size requirements. It's great if you can plant trees that are good for more than just the screening you want. Wildlife habitat would be great, or food you can use or sell for example. Once established, native trees can offer habitat and food for wildlife, and wouldn't need any supplemental water. You would have the choice of letting them grow naturally or keeping them pruned.

Where in AZ?

Check out what is growing in the wild and plant that species, and pamper it . That's your best bet for a no-hassle screen planting.

There are several types of Pine trees that may work.

We used to put in "Silk Oak" trees. They are messy BUT they grow full and would hide lots from view.

Thank you all for the input. There is not too much here other than mesquite - which we don't want because of the thorns, Oleander - which is out because of the kids and dog. What is left is desert willow. I guess we could try that or perhaps some pines?

We are in unincorporated Cochise county, about 20 minutes from Tombstone.

I found something that might be useful to you, a list of plants for Cochise County based on size and water use. Depending on how tall you need the screen to be, you might be able to use a large shrub instead of a tree. It also tells you which plants on the list are natives.

Here is a link that might be useful: Low Water Plants for Cochise County

I did some bird-watching down around Willcox (Wilcox?) last winter and noticed that many homes were surrounded by thickets of Elderica pine and AZ cypress, presumably as windbreaks.

They looked to be thriving in that climate, and the cypress in particular looked to be a good screen. The cypress is native; the pine is not if that's of concern.

Thank you. This has all been very useful. There look to be some good choices available.

You've gotten great answers! Let us know what you select and how it works out. My first choice would be hopseed (Dodonaea viscosa) which grows fast, is evergreen, native, and provides great visual/wind/dust protection AND it's very low water use once established. It will easily reach fifteen feet in height. Twenty? Probably. It also tolerates trimming/pruning and even shearing. You can push it into fast growth early on with a bit of water and then ease the water off over several months to a year to harden it off to infrequent watering when it's the height you want. Just don't overdo it so much that the plants are too weak when given a high water diet.

Good luck and keep us posted!
Take care,
Grant

Here is a link that might be useful: hopseed link (one of many)

Pomegranates?