It's an annual, unlike Glechoma hederacea, but it reseeds like mad. Your speedwell lawn could take several years to clear if it has been allowed to seed. (Which it has - I can see the pods). It will germinate even in the winter in mild spells.

Interesting and sincerely thank you for the link. Please don't take the following in any way personally, just my unmitigated disgust that I pay for the USDA FS. I always thought that EI was benign. Then again, before reading A Walk in the Woods by Bill Bryson, I thought that the Forest Service was as well... Anything with their logo on it makes my gorge rise: "About 240 million acres of America's forests are owned by the government. The bulk of this - 191 million acres, spread over 155 parcels of land - is held by the U.S. Forest Service under the designations of National Forests, National Grasslands, and National Recreation Areas. The Forest Service is truly an extraordinary institution. A lot of people, seeing that word forest in the title, assume it has something to do with looking after trees. In fact, no - thought that was the original plan... In fact, mostly what the Forest Service does is build roads. I am not kidding. There are 378,000 miles of roads in America's national forests. That may seem like a meaningless figure, but look at it this way - it is eight times the total mileage of America's interstate highway system. It is the largest road system in the world in control of a single body. The Forest Service has the second highest number of road engineers of any government institution on the planet. It is the avowed aim of the U.S. Forest Service to construct 580,000 miles of additional forest road by the middle of next century. The reason that the Forest Service builds these roads, quite apart from the deep pleasure of doing noisy things in the woods with big yellow machines, is to allow private timber companies to get to previously inaccessible stands of trees.... Eighty percent of its leasing arrangements lost money, often vast amounts. In one typical deal, the Forest Service sold hundred-year-old lodgepole pines in the Targhee National Forest in Idaho for about $2 each after spending $4 per tree surveying the land, drawing up contracts, and, of course, building roads. Between 1989 and 1997, it lost an average of $242 million a year - almost $2 billion all told, according to the Wilderness Society." (P.46-48) Here is a link that might be useful: Forest Service

Check out Commelina. There are a few native perennial species and a widely naturalized Asian annual species found in the US.

A nearly infinite list of plants could be generated by your question, especially in lovely zone 7. Most plants will increase their size in some way. As a general rule, though, plants to avoid are those that produce runners or copious amounts of seeds. Do you have a bloom color preference? Height preference? Any issues with drainage, rabbits, deer? Do you prefer fragrant flowers? With the number of plants that fit your initial request, you can afford to be much more specific. I might recommend getting your own personal copy of "the bible" - The Well-Tended Perennial Garden by Track DiSabato-Aust, or at least check it out of your library. My other favorite book is Botanica's Annuals & Perennials. This is the most comprehensive list of flowering (2,000) plants I've ever seen, with pictures of most. In the past, I've never had the results I wanted by starting my planning with the question "what do I want?" The chances of finding those particular plants in a store near you are not always good. Lots of people do it, but I'm not comfortable ordering plants from faraway places by mail or internet. So I find it's best to shop around, see what's available, then decide "which of these plants do I like?" From there, you can determine which of those would perform to your satisfaction in your garden.