Hi, the artemisia can be cut back hard in spring, but the Hebe should only have a light prune, to keep the shape, however if it were mine, I think I would probably try cutting back a few shoots at a time, and see what happens, it should eventually recover, if that works, you can cut back the other shoots next year, Derek.

I agree with Derek re the Artemisia and sort of agree about the Hebe.
I'd remove a 1/3 of the Hebe but obviously not all from one place. This way you will keep the shape. You could also use the prunings to see if you can propagate more of them just in case it isn't happy about the prune.

Agree re the Hebe. I have cut back quite radically but not all at once.

Thank you all, I'm pleased the Artemisia can have a good haircut and reshaping; behind it is the Hebe. I'll leave it for a couple of weeks, then we'll really be into Spring.

Thanks once again..

Sometimes hebe can be hard pruned, but on some it can be painfully slow to respond, one way to deal with this is to bend down a good bunch of those long shoots, dig a small hollow and bury them, put a stone on and leave for a year in which time they will have rooted then cut from parent plant and there you have a new plant that can be trimmed over the years to keep compact, this always works well.