It is common for utilities in desert areas to take a two fold approach to managing vegetation in desert areas. Two different herbicides are often used, one for urban/residential areas and another for more rural areas.

Rural area treatment options:

Herbicide: Topsite

Manufacturer - SSI

Active ingredient - imazapyr. and Dyuron

This herbicide helps reduce off target damage as it is designed to stays put in the soil. Also, Topsite is not very soluble and doesn't leach into ground water and will not move down slopes unless there is a heavy rain. The active ingredient Imazapyr half life is 120 days. The active ingredient Dyuron half life is 80 days.

I want to stress that this product should only be used in rural areas to avoid potential damage to off target vegetation.

Residential

Herbicide: Pendulum 2G

Manufacturer: BASF

An application of 2 pounds per 100 square feet should be sufficient to control vegetation in residential areas.

As with any herbicide program, it is important to carefully document your applications and audit completed work for effectiveness.
Give these two herbicides a try and you will most likely see a dramatic improvement in the control of vegetation around wood poles in your area.