Need shrub/tree identification from empty lot in East Austin, TX - Zone 8

This is a tree covered lot with lots of Spanish Oaks and Cedar Elms. Between the trees there are many of what i would call shrubs. They are everywhere. You can't even walk around without cutting them down. They grow in clumps and the 'trunks' are narrow like a pool queue, sometimes a bit thicker, sometimes a bit thinner. They can grow up to 20' tall.

Thanks in advance,
-Craig

 

Opposite branch arrangement suggests Privet. An image showing scale and a different background
color might change that though.

 

Thank you, saltcedar. It was my suspicion, and the wikipedia article supports what I see.

Best,
-c