After a brief experiment with it in the garden, plume poppy (Macleaya cordata) has earned a place very high up on my Most Invasive Plant list! I was aware that it was considered invasive but I thought I'd try one anyway and see for myself last summer. It didn't do much of anything at all last year and this spring, I was even wondering if it had survived... but then yesterday I noticed the distinctive leaves coming up 1-2 feet away from the plant. Upon starting to dig, I found the roots going out even farther - truly impressive! I wish I had a confined space for it but lacking that, it's in the composter.
A similar story with Stachys lavandulifolia in the rock garden... Though the flowers are very beautiful, it seems to have spent most of its energy sending shoots far and wide instead of flowering, so it's been turfed too. The roots went extremely deep and it will no doubt will keep popping up for some time.