Remove the trunks that fail to produce flowers and leaves in spring, a sign the wood is dead. Cut them back to the base of the plant. Look at the stems that sprouted on the live trunks. Chop back to their point of origin any overgrown twigs blocking pathways, windows or developing toward an area you want to keep free of branches.
Prune the entire plant back to the base in a method known as "coppicing." First, research your shrub species to find out how it responds to severe pruning. Elderberries and ninebark, for example, recover well. Ask the county extension office or the staff at a local nursery if you are not sure how your bush species responds to heavy pruning.
Thin the overgrown shrub, cutting 1/3 of the upright trunks to the ground. Chop down dead and crisscrossed stems first. If they amount to less than 1/3 of the bush, remove the largest healthy trunks. Aim at putting 2 inches of space between every two upright stems. Prune nonflowering plants and those that bloom in the summer in early spring. Wait for spring blossoms to fade before trimming a shrub's branches.