Vinca minor?

Privet, Ligustrum species.

Yep, looks like Chinese privet.

Yes - Chinese privet (Ligustrum sinense) would fit well. A leading bird-spread invasive in the Dallas area. Glad to know what it looks like up close.

Thanks for the help!

Here is a link that might be useful: Dallas-area naturalists trying to halt Chinese privet's spread

You say 'small leaved' plant. What size are those leaves exactly? Is that Texas small, ie quite big,or normal small? Does Lonicera nitida grow in Texas?

I thought of box honeysuckle also; maybe it is one of the smaller leaved evergreen privets - one other than L. sinense. Otherwise it sure looks like a Lonicera.

Why do you guys think it is not chinese privet? Looks just like it to me and I see it every day!

Looking at the fence boards and the grass as the only means of gauging scale the leaves seem rather small. I am the opposite to you esh_ga - I never see Chinese privet but I see Lonicera nitida a lot. It was only a suggestion and until the OP comes back with a measurement I am certainly not sure.

Most of the remaining leaves are in the 2.5 to 3.5 cm range. Because the largest leaves in the original photo were devoured, I'm guessing the longest was around 4.0 cm. In Texas parlance, that's "smaller than a live oak's, but bigger than a yaupon's". For reference, the fence boards are about 3 3/8 inches wide.

Don't recall seeing lonicera nitida around here, though our hardiness zone is okay. Must be other reasons there's little or no mention on area university or nursery web sites. Appears more common in the US Pacific Northwest.

EDIT: Added link to a fact sheet which gives leaf length for Chinese privet in the range of 2 to 5 cm.

Here is a link that might be useful: Ligustrum sinense fact sheet

This post was edited by bostedo on Wed, Oct 23, 13 at 21:59

Never seen it here, so it's most likely rare or non-existent.

OK, the size eliminates the Lonicera.