Thanks for your input, Tracy and Alana.
It is true that tree peonies can take pruning - I have been pruning the pink one for years since it tended to be a fast grower. The white one had more of a lateral spread than a vertical growth, but it is time to prune.
I have a question for the two of you - have you ever successfully rooted any of your tree peony cuttings? I have just stuck the stems in some potting mix every now and then, but would always forget to keep the soil moist so the cuttings die. If I know that they can be rooted with a little care, I may make more of an effort.