Move the branches of the bush to get a better view of the center of the bridal wreath shrub after all flowers have finished blooming. Each cluster will have a yellow-brown color. Check for dead and broken branches within the bush.
Cut away each cluster of dead flowers with pruning shears. Snip the entire tip of the branch to remove the complete set of dead blossoms. This cleanup should be done each spring to allow the plant to feed on the nutrients in the soil throughout the summer without losing nutrition to the flowering portions of the plant.
Cut any broken or dead branches from the bush at the bottom of the plant near the ground. Make sure to remove these types of branches every year. Pile the branches to the side of the bush or in a wheelbarrow until you can remove them from the area for disposal. This is a precaution against entangling your feet in the refuse as you work.
Remove any branch tips that have become overgrown and are so long that they block a pathway or interfere with another bush in the border or garden. An over-sized spirea bush can choke out flowering plants and shrubs.