Prune your royal poinciana tree during its first three years to encourage strong branches. Remove all suckers--stems that sprout from the side of the tree--as well as limbs that are less than 8 to 12 feet from the ground. Remove branches that are dead, dying, broken or crossed, and prune to open up the center of the tree in order to increase sunlight and air circulation. Cut back growing tips to limit height and width, if desired.