Answer: It is a characteristic of mesquite to grow quickly, especially if they are given too much water. You didn't say how long the trees have been in the ground, but once established, they can be watered about once a month in winter, twice a week in summer. Water should penetrate slowly and deeply through the entire root zone. If they grow too fast, they can develop weakly attached branches subject to breaking. Newly planted trees should not be pruned for at least one, or even two, years. The idea is to leave the lower branches on, as they help the trunk develop girth and stability. So, assuming your tree is relatively young, I'd leave it alone. You should not have to prune again so soon.
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