What to do about lily-of-the-valley?

I am saddened by my discovery that lily-of-the-valley (Convallaria majalis) is non-native and somewhat invasive. The scent and flowers are beautiful, and it fills shady spaces perfectly. But I guess I can't in good conscience use any more of it. Fortunately at present it is only in two fairly contained parts of the yard where the rhizomes have nowhere to go (except into the lawn from one area, and under a fence into a neighbor's garden from the other). I can't bring myself to consider ripping it out, not with so many other nastier species to worry about. I'm pretty sure birds don't spread the seeds given that they are toxic, and aren't produced in large quantities.

6/3/14

My hope was that mine would turn out to be the American sub-species rather than the European one, in

European columbine?

I'm pretty sure I figured out what this is: European columbine (Aquilegia vulgaris var. Stellata, possibly 'Blue Barlow'). The leaves are definitely columbinish, but the upside-down flowers are completely different from the native columbine I planted. I assume it was planted deliberately, but I only noticed it a year or so ago. Supposedly it doesn't last more than a few years. It is non-native, but very pretty, so if it self-seeds I will keep it around.

5/26/14

5/26/14