From the flowers it appears to be a speedwell (Veronica).

Thanks for the suggestions! We don't like grasses in the yard, especially after helping our neighbor get rid of some really, really invasive grass that Urban Gardener planted in their yard this past year. We have a lot of shrubs in the area already, and are looking for something more low-lying (less than 2"-8" tall) to fill in. I've never really had a thing for mondo grasses, but we all have our loves :) Between the three spreaders/clumpers above (veronica, epimediums, partridgeberry) we should be able to work something out to cover at least 60-70% of the area in question, which would mean 60-70% less weeding, and something to keep the ferns company during the winter when many of the other things have died back. I don't mind spending $$, I'm totally fine with that, but ... I don't want something that is a tiny 6" clump at full size, else we will be seriously spending a thousand dollars buying 200+ plants to fill the bed. Are the three aforementioned species relatively safe to plant near perrenials that die back down to the ground every year and re-sprout, or will they choke those out? If it is not safe, what kind of spacing should I be trying to maintain between these and other plants? (i.e. would the average spread diameter + 6" buffer be adequate?) I am normally really wary of non-native species, seems like most of the common ones are too invasive for my liking, which is why I had to ask. Search was turning up a ton of results, but I couldn't seem to refine it enough to find meaty info. Thanks again for the advice! BTW - Epimedium warleyense and versicolor flowers both look amazing! (see pics halfway down page)

I have this growing in my woodland (mine looks more like the one called African Club Moss) and I tried to transplant some to an old growth rotting log. It died. I have quite a bit of it so I might try it again. I really like this moss. It just appeared one day and I have kind of nurtured it. Most of it is growing in whats left of an old compost pile I didn't get around to moving. So it seems to like it on the rich side.

Many years ago-we've been in the same little house for decades now-I did in fact rid my lawn of all broadleaf weeds including Glechoma. It required two apps of phenoxy herbicides, about ten days apart, but it did work. Of course, all the planting beds along the border and really, just the lawns themselves allowed the stuff to come roaring back from adjacent low-maintenance yards. The takeover is now complete, from one end of the yard to the other. That, along with wood violets and other assorted weeds including clovers comprise most of my lawn at this time. I've learned not to care. And again, with my newest baby granddaughter living in an apartment we own right above our house, the occasions for that little one to be out in the grass playing are numerous. Right now, that takes precedence over having a weed-free lawn. In fact, it's not even close!