See important note from Cliff about girdling added below
The Balcones Canyonlands Preserve protects a diverse ecosystem that supports endangered and rare songbirds, cave invertebrates, many rare plants, and aquatic salamanders (www.austintexas.gov/BCPstory). Protecting the habitat of these species includes controlling invasive plants. Invasive plants are nonnative (meaning they come from somewhere else) AND cause harm to native ecosystems.
For Glossy Privet trees that cannot be removed with a weed wrench, this video demonstrates a nontoxic method known as “girdling”. This method allows native seedlings to establish and replace the Glossy Privet canopy as these nonnative trees slowly decompose.
For more information on how to identify Glossy Privet and other invasive plants in the Austin areas, see https://www.austintexas.gov/sites/def...

To learn more about the many benefits of native trees and how to plant a tree, check out our Forest Restoration webinar series:    • Balcones Canyonlands Preserve Forest ...  

Important note from Cliff (added 3/8/2021):
When you're peeling the bark and phloem away from the trunk, you won't see the difference in color that shows up in the video. On camera, the beige shade of the exposed sapwood and the bright white of the phloem are easy to distinguish. With the naked eye, both seem to be ivorycolored. It's easy to miss seeing that you left a lot of phloem behind. On the other hand, if you leave the girdled trunk alone for a few minutes, both the phloem and the cambium on the surface of the sapwood will darken. Better yet, they will darken to different shades of brown. Then it's easy to see what's left and to know when you've finished removing it. So when I girdle a multitrunked tree, I will do all the work with each tool before going to the next tool:
1. Circumferential cuts with the carpet knife—on every trunk.
2. Peel away the bark and phloem with the putty scraper—on every trunk.
3. Now that the trunks are darkening, start with the first trunk I peeled and do a quick followup scraping to remove the big pieces of phloem—on every trunk.
4. Starting again with that first trunk, scrub with soapy water and a coarse scrubbing pad—on every trunk.
5. Again, starting with that first trunk, scrub with rubbing alcohol (70 percent isopropyl alcohol; check the label) and a finer scrubbing pad.

If a tree has only one trunk, I will girdle several other trunks at the same time, working through the same sequence. By giving each trunk a few minutes to age between steps, I make it easier for me to see the tissue I need to remove.