Answer: Ornamental cherry trees do not usually need much pruning. The exception would be to remove any suckers from the roots or shoots growing from the trunk below the graft. These should be removed as soon as they appear. In addition, you would remove broken, damaged or diseased branches as soon as you notice them. Pruning leaves wounds that are open to pests and diseases, so minimal pruning is usually preferable.
Orchard cherry trees might need some specialized pruning to help produce a better crop. The following guide from Penn State will help you.
Good luck with your new cherry trees!
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