As much as I anticipate the fall with its slanting golden light, vivid leaf colors, and cooling temperatures, there is one aspect of the season that I find discouraging. When I look at the sad state of the garden perennials and shrubs, I see only ragged, leggy, bug-eaten leaves and droopy, dried-up flowers. I want to turn around, go back in the house, and shut the door until April.

This blue mood doesn’t last too long, though. I know there is cleaning up to do in the garden beds, and this year I need to divide and move several peonies that have formed an impenetrable grouping in one bed near the house. I have plenty of room for the divisions in a border where we plan to remove some towering daylilies that dwarf the surrounding perennials.

Before we delve into the specifics of dividing peony plants, let’s take a look at some general information on dividing perennials. Many perennials should be divided every three to five years, or when they are producing smaller flowers or sparse...