I find it works best to cut lavender back in early spring, just as it is starting to leaf out. Cut it back hard - I remove 1/3 to 1/2 of the plant - and the new growth will cover up the older woody stems. You'll never get rid of the woody growth because that's just how lavender grows, but with pruning you can keep it mostly hidden. And, hard pruning encourages more flowers - the best part of the plant in my opinion.

I thought, too, she must be really busy. I don't think she's been to tea for a month. On another note; when are people going to clean out their old stuff and replace it with their new Christmas stuff? I've been watching craigslist and there's nothing.

I believe we're in the Rubiaceae. Maybe Sherardia? No idea which species you'd have in Texas. Has S arvensis got there?

"I would caution planting them adjacent to wooded or natural areas as they can spread quite freely": Agreed. This is in the middle of a city and away from wooded areas. I'm going with "Vinca minor" from that comment, and also from my searches on the web, some links of which are attached as comments to that Google photo album link. Since I have the english ivy (which is X'ed out in red in one of the photos) to remove, I will proceed with propagating these in both sunny and partially shaded areas to see what takes and what doesn't. In this area, the Willamette Valley, we get tons of rain yet it is holding up just fine (well in this shaded area; I don't know yet how it will hold up in the sunny parts of the property). Thanks for everyones replies!