GGG, not sure if this is unusual enough, but how about Rubus 'Creeping Raspberry'? Does great in full sun and is drought tolerant.

How about Rubus calycinoides? Interesting thick textured leaves about the size of quarter. Flat grower with soft prickles along stems but not too prickly to work around. Turns lovely shades of red to burgundy in Fall. I've never seen blooms but I cut mine often for arrangements. Also mine now grows in container so it might bloom and set fruit if in ground.

Perhaps Saxifraga sarmentosa, also a nicely textured ground hugger with half-dollar size leaves on thin red stems, with delicate white flowers about 10" tall in spring.

The dark purple cultivars of Ajuga do well in sun but don't spread as fast as the above two, which might be an advantage.

All of these are not that unusual but are easy to grow and yet easily controlled shallow rooters. Also can stand up to occasional foot traffic. I rather like the idea of using more than one groundcover to add interest contrast in winter. In summer your other plants will take over. josh

Here is a link that might be useful: Rubus calycinoides

Um, I'm really looking for something unusual. I do have all those particular groundcovers already, which are considered fairly common.
It's hard to list all the groundcovers I have. There are a LOT, lol. I don't like to see any dirt. I just want to see plant...and a huge variety of them.
Josh, I like the idea of a rubus in a container. That might work great as a containerized perennial for shade. Thanks for the idea!

GGG

I don't have anything unusual either but I do like dianthus gratianopolitanus and creeping veronica very much.

I like partridge berry (Mitchella repens).

Here is a link that might be useful: {{gwi:843871}}

GGG,
you probably already have that creeping veronica, I think it's Georgia Blue, but if not and you'd like to get some of mine, you're welcome to do so. I think it's safe to call it evergreen. And it definitely doesn't need to be watered. However, I think it will crowd out anything else (it seems to be crushing some ajuga that was growing near it in my flowerbed), so if you're wanting a loose groundcover that other flowering things can grow through, it might not work.

Let me urge you to order a native evergreen Georgia plant from Plant Delights that I know you will love and is perfect for your situation. It is the Georgia Savory (Clinopodium georgianum coll.) It was new to me two years ago and the little rooted cutting I planted in hot sun and drought is now a circular 24" clump of dense growth that inhibits weeds. The foliage resembles Rosemary and the fall/winter light lavender blossoms also look like Rosemary blooms. It grows about 8"-12" high and then the outer branches lie down and new growth comes from the middle of the plant. So, as it matures it really is only about 7" tall.
I would guess that in time it self roots and continues spreading although it would be easy to control. I cannot rave enough about this savory for heat, blinding sun and adverse conditions. Anyone trying to hold a sunny slope should plant this one. I found cuttings easy to root just tucked in a pot of soil, left in the sun and kept moist. Hopefully you will order one. It's a winner!

Nandina, the clintipodum hated my garden! Do you have red clay? Even in partially ammended clay the poor thing kicked up a fuss. It got sopping wet in the spring, then try as a bone after that....the dealth of so many beauties, even natives. It is however, a very good suggestion. I am adding some builders sand to an area for a plant that needs really good drainage and more sandy soil. Maybe that would be a better place to put this little one?

Westy, if you think the veronica can take no extra water and baking (or sopping) clay, then I'd love to try some. I can plant it in an area like around the mailbox so that it won't bother other things.

GGG

I once had a patch of Verbena peruviana in a sunny spot that was beautiful. It died out due to encroaching shade.

The plant lies as flat as any can. I believe a piece of paper lying on the ground is taller! Only when in bloom did it reach 2" tall! Tiny, but very dense foliage, accentuated by very dark red flowers. It was hands down the best looking Verbena I've ever grown. I had it for over 5 years before the shade got it. If I had any opening in sun now, I'd grow it again in a heartbeat.

How about crown vetch. It is an evergreen and gets pink flowers in late spring. It also chokes out weeds.
Cookie

I always thought Crown Vetch WAS a weed!....and invasive.

I would think the only thing that would last out there would be some different varieties of Sedum, hardy Cactus, or maybe Mazus, Thyme or Ice plant. Not really different plants but, good survivors.

GGG that seems like an area for some tried and true survivors, maybe you can move some of your hardiest ground covers out there and replace them with something more exotic in an "easier" spot.

GGG,
we've got a 3-day weekend beginning tomorrow; I'll bring you some of that veronica. I think it's worth a try.