I have a small Serviceberry/Shad Tree (6 ft tall) that I planted a year ago. The tree isn't full enough to provide much shade to the area underneath it yet. There is a rock border around the base that is about 4 feet in diameter. This spring I planted some Irish Moss in the area because I know it's supposed to like full sun, but it didn't make it. I don't know if the clumps were too small or what (I had 6 clumps about 2" around each). Anyway, maybe it'll come back next year but I doubt it.

I would like some very low (a couple inches preferred) ground cover, with or without flowers for this area. The hardier the better, since I'm not much of a hands-on gardener. But I don't want something that will spread like crazy past the rock borders and take over the lawn. Thanks for any suggestions!