Answer: You can prune away any dead wood at any time of the year, but to prune and shape your olive trees, you'll want to prune in the early spring, just as new growth begins. Dead shoots and branches are common with trees and as long as there are only a few, there's nothing to worry about. If you're seeing more and more dead wood as the season progresses, then there might a problem and you may want to have a professional visit your landscape and assess your trees.
The major pruning rules are fairly simple - prune early in the season so the tree has all summer to grow new branches and leaves; never remove more than one-third of the live growth at any one time; and, don't leave stumps - prune close to the branch or trunk of the tree without leaving a stub. Aside from that, remember to water your olive trees on a regular basis and they should grow into healthy specimens.
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