My yard, which was never in great form, is a complete disaster with
this extended dry hot weather. I'm in Nashville, TN, Zone 7, clay

About the only thing I can think of offhand is Callicarpa americana,
beautybush, though it'll grow more than 3 ft over time. Not difficult
to prune, though.

Peonies might work for you, too, but they're not natives.

Remember, even drought-resistant plants need to be watered until they're
well established.

However, if your clay is expansive, you might be better off putting in
drip irrigation around the foundation, to keep the soil (and your slab
or basement) from heaving with changes in soil water content. This is
pretty commonly done in Texas, but I have no idea if it's a good idea
in your part of the world or not.

A commercial site that talks about this:
http://www.foundationwatering.com/canwesolve.aspx

Your soils extension folks and/or the civil engineering folks should be
able to tell you if this is something needed in your area.