The ideal form for most large shade trees is a single central leader or trunk with scaffold branches spaced at intervals vertically and radially around the trunk. Once the tree has reached sufficient size, all branches below a height of 6 or 7 feet are removed to allow easy walking under the branches. Some small ornamental trees may have the lowest branches at a lower height. If more than one major upright leader develops because the single central leader has been pruned or broken, then all but one should be removed or shortened by at least half. Keep the straightest upright branch for the central leader, even if it is not the largest. Some trees have a natural form with multiple leaders and should not be trained with a single leader.
When scaffold branches are too crowded and grow into each other, keep the branch which has an angle with the trunk closest to 90 degrees. Narrow crotch angles of less than 45 degrees are weaker and easily broken. Side branches off the scaffold branches which are growing in toward the center of the tree or are growing into each other are usually removed at their source. When shortening branches, prune just above a side branch if possible. If no side branches are present, prune just above a bud. Stubs left above buds or branches will die and are an open invitation to rot and insects.
If you would like help pruning trees, give me a call. I can prune them for you or teach you how to prune them yourself. There is no charge for an estimate.