They heavy clay may be a problem but it can't be too bad if the bleeding heart will grow there. I haven't had success with my heavy clay soil and bleeding heart.

Here's a quick list that I can think of:
dead nettle esp White nancy
bishop's weed
hostas -- you'd probably need to water until established
vinca (periwinkle) blooms about the same time as the bleeding hearts That would be kind of pretty together
some of the ferns but they can get ratty in midsummer too.
some of the dayliles are pretty tolerant of shade. I have the old-fashioned daylily that we call ditch lilies here in Iowa along with some indestuctable fern on the north of my house. Be warned both of these spread. We call them ditch lilies because they fill the ditches where old farmsteads used to be. the invasiveness is worse when they are in sun.

I remember there was a thread a while ago on invasive ground covers for dry shade. Are you looking for a ground cover or something that bushes up and hides the tired bleeding hearts? Vinca and dead nettle don't grow tall.

I'm sure lots of other people can come up with a more comprehensive list. Good luck. mmo

I have heavy clay soil here too. I've planted a couple Japanese Painted Ferns on the north side of the house. They do very well there and don't seem to spread. I also like some of the smaller hostas with lots of white in their leaves. Both of these look very nice with the bleeding hearts. I put a few Rozanne hardy geraniums along the front edge of the border. They look more like a ground cover with their "winding" ways but are not invasive and bloom like crazy right up to the first hard frost.

Good luck with whatever you plant!

Thanks for all the suggestions - I will look into them more. I'm not really sure if I want groundcover or something taller - I just know that the bleeding hearts are looking pretty sad right now and I'd like to improve the look on that side of the house.

There is nothing like a snowball hydrangea with a bleeding heart. I have them close together and beautiful. As my bleeders shrival, the hydrangeas explode. In Minnesota we are in a drought too and the hydrangeas are looking great. Its also maintenance free too. Zone 4

Thanks for the recommendation on the snowball hydrangeas! How tall do they get for you, and do they die back to the ground each year in zone 4? I saw some today at a local nursery, and they were very pretty, but $30 each . . . I might have to buy some smaller ones online I think!

Astilbes, Lily-of-the-Valley, Hostas & Ferns