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Shrubs like hydrangeas or barberries, and trees like cherries, spruce, and poplar, are best when pruned in the winter. This allows you to better see the branches since they won’t have leaves.  Other shrubs include mallows, camellias, glossy abelias, and European hornbeams. Trees like crab apples, junipers, plums, honey locusts, and bald cypresses should also be pruned during the winter. Some trees will leak sap onto the ground or your car if you prune them in the late winter, so aim for cutting them back in the summer. This also includes trees such as walnuts, elms, and dogwoods. Signs of dead branches include leaves that are shriveled up and brown and branches without any leaves on them while other branches have green leaves. If you see a dead branch, use sharp pruning shears to remove the entire branch.  If the bark has fallen off, this could be another sign that the tree is dead. If there's a discolored spot on the tree that turned yellowish or brown, it's likely that it's dying. To check, you can scrape the bark and look for a green color beneath it, which means the tree is alive. For larger branches, use a hand saw. If your tree has a diseased portion — such as a fungus on its branches or strange spots on its leaves — prune below the diseased section to remove it.  Wait until it isn’t wet outside to prune, as water will spread the disease. Clean your pruning shears between cuts with rubbing alcohol to kill disease and stop it from spreading. Make sure to do this before starting on another tree that has no signs of disease. If 2 branches are crossing, cut the smaller branch so that they’re no longer in each other’s path. You want the branches to continue growing outwards, so cut right above an outward facing bud to ensure it keeps growing out. Do not cut right above a bud that’s facing towards the middle of the tree because it will make the branch grow inwards. Keep branches that are growing outwards around a 45 degree angle. Try to eliminate unnecessary branches that are growing inwards at an odd angle so that the whole tree or bush can have access to sun and fresh air.

Summary:
Prune summer and fall flowering trees as well as shrubs in the winter. Cut back trees like maples and birches in the summer to prevent sap leaks. Remove any dead or dying branches first. Remove any diseased branches you see. Look for branches that are intersecting one another. Thin branches so that sunlight and air can reach the center of the plants.