I spend a lot of time every year keeping them (and their dozens of offspring) under control and I've finally had it with them — I want them gone.
This is the current state of the largest of the bushes: a 6"/15cm high stump, about 16"/40cm by 12"/30cm with four large trunks. The other bushes have smaller trunks, but they'll be in a similar state as soon as I can get the time to cut them back.
However, in the time I've been in this house, ice storms have knocked them back to the ground twice; they regrow just fine once the weather warms up, so I know they're tenacious.
A complication is that my sewer and gas lines both run along that side of the house, so I'm limited in the digging or picking I can do there.
What do I have to do to get rid of them for once and for all?