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The ideal time to prune a crabapple tree is late winter or early spring, before the new set of leaves begin to appear. You can also get away with pruning in mid- or early winter, though this may make the tree more vulnerable to cold-related injury.  Hold off on pruning your crabapple tree until after the first killing frost of the season to ensure that it has gone dormant.  In a pinch, it’s okay to prune in early summer after the tree has finished blooming, although this can increase the risk of "fire blight" and other warm-weather diseases. Aim to have your pruning finished before June (or December, if you’re located in the Southern hemisphere). One of these tools will make it easier to get through thick branches and stems. Chainsaws offer more power for quick and easy trimming, while handheld saws allow for greater control so you can only take off as much unwanted growth as you need. It may also help to have a pair of telescoping loppers to remove smaller stems and offshoots high up in the canopy of the tree. Start by notching the underside of the targeted branch 4–5 inches (10–13 cm) from where it meets the trunk. Then, make a second cut 2–3 inches (5.1–7.6 cm) further out on the limb, this time sawing all the way through. Go back and remove the remaining stump at the collar, or the thick section where the branch grows out the trunk.  The first undercut you make will prevent excess bark from peeling off the trunk once the limb comes free.  Avoid cutting perfectly flush with the trunk. Insects and disease-causing organisms can easily find their way into the tree through open wounds in the trunk. Inspect the tree for branches that are rotting or appear brittle and colorless. When you find an affected branch, remove the entire limb at its collar.  If you're unsure whether particular branch is dead, scrape the wood with your fingernail to remove a portion of the bark. If the flesh is underneath is green-white, it’s still alive. If it’s brown or black, it’s most likely dead. Keeping your crabapple tree free of dead wood is a good idea at any time of year, since it’s more likely to introduce disease. Occasionally, a branch will begin to twist in on itself as it grows, reaching back toward the center of the tree rather than out from the center. Saw these branches off close as to the collar as you can without accidentally cutting into the trunk itself or other nearby branches. Removing inward-growing branches will give the tree a neater, more uniform shape. Similar to inward-growing branches, it’s possible for some branches to become entwined or compete for space. To get rid of branches that are already crossing, take off both branches where they connect to the trunk. For branches that are growing close together but not yet crossing, you can get away with only removing one branch. If you decide to remove only one branch, single out the one that looks weakest or most awkwardly placed. Low-hanging branches can sometimes interfere with walking, mowing, or other activities that require you to pass beneath the tree. If this is the case, you can deal with them the way you would other large branches by sawing them off close to the trunk.  Remember to make your cuts as clean as possible so that no stumps remain. If your tree’s lower branches aren’t causing a problem, it’s usually best to let them stay.

Summary:
Do your major pruning during the dormant season. Use a pruning saw or chainsaw to take care of heavy pruning. Cut large limbs where they connect to the trunk. Clear out dead or dying wood first. Cut away inward-growing branches. Trim branches that cross or are growing too close together. Thin out the lower branches if desired.