Aquilegia, unless I want the seeds I will dead head - but I cut the entire plants - all the leaves, everything, down to the ground! It looks a bit drastic but you get lovely fresh new growth in a week or so.

The bay is more tricky, think I would only trim those stems that are not in the right place and leave the rest. It sounds like it needs some TLC rather than pruning, so once it's repotted and has lots of lovely feed it should start to grow new leaves.