Lamium is a good ground cover. It also has a bloom. Foliage will pick up the light. Intersperse with some Astilbe for a plume type flower. It will give you some more interest. Both can take some morning sun and are great for afternoon shade. The Lamium can be mowed back if they creep out of their area. Astilbe is low mounded with spikes of plume like flowers. They come in Red, Lavender and White. Thier foliage is serated and dark that becomes more bronzed on the edges as the season wears on. Hope this helps!

I'm assuming you'd prefer something evergreen.

Would there be enough sun for Blue Rug juniper (or one of the other prostrate junipers)? It's not really quick-growing (I've seen both 4-8" per year and 1-2', but the first seems much more likely). However, in a space only 2 1/2 - 3' wide, it wouldn't really need to grow very fast.

Then there's creeping phlox -- I don't remember if it stays evergreen in the winter or dies back. Here's an old thread I happened on when I was looking to see if creeping phlox would overwinter in your zone:
http://forums.gardenweb.com/forums/load/grdcvr/msg051607367598.html

Regardless what you decide on for a groundcover, while it's growing in you might want to use a pre-emergent to keep the weeds from sprouting. Corn gluten is a non-chemical pre-emergent; it's the ingredient in Concern and the organic version of Preen. I've seen both at Lowe's.

How about paving the area with something that will smother the grass.

I too thought first of juniper - it's my favourite look for such a situation. But they might not be ideal facing east, unless it gets sun from both sides. There are several kinds, really flat creeping and mounding, ranging from gold (Mother Lode) to blue.

But you do actually have enough room for a nice garden bed there; why write it off, and why dedicate it all to one plant? I shudder at the idea of the invasive ground covers; it's only trading off one nightmare for another - and even if they do work and are well enough contained, most of them are ugly and monotonous - why have that next to your deck. The only one I would actually like would be bergenia. That carpets very nicely in time, and due to its big leaves, shades the ground and suppresses weeds quite well. You could use different types for variety.

The trick is indeed to cover the ground, but don't confuse that with having to have "ground cover" plants that spread by runners or stolons. You need plants whose leaves will shade the ground beneath. Something like a variety of huge, big-leaved hostas would be perfect, and east should be a good exposure for them. If you want recommendations, ask at either your local nursery or the Hosta forum. Intersperse with other good ground covering plants, including hellebores and ferns. Bergenias too, actually, you don't have to let them take over.

Your clumping plants, like hostas, may need to be divided every few years to ensure they don't push on the wall, but that's less work than weed-whacking.

Do you even have to keep it low growing? It sounds like the kind of place I'd even put some smaller shrubs.

KarinL