This shrub has been growing in my garden for the 42+ years that I've lived there, but I have no idea what it is.
Agree with thanrose. SPIRAEA prunifolia. http://www.missouriplants.com/Whitealt/Spiraea_prunifolia_page.html
Thanks for the help. I had seen spiraeas with flat clusters, and it hadn't occurred to me that this could also be a spiraea.