Answer: The Brazilian pepper is one of those trees not adapted to the desert. It will respond to heat stress by dropping its leaves to minimize transpiration (the loss of water through evaporation). The best way to tell if your tree is getting enough water is to dig down around the trunk and see how deep the moisture penetrates. It should go down at least a foot. Also, since your tree is established, make sure your emitters extend out away from the trunk to the tree's drip line.
If it is on a drip system, next summer try watering four or five hours at a time twice a week and see what happens.
You can prune your brazilian pepper tree now, in late summer. Don't prune it back as much as you would a mulberry tree - it won't respond favorably. Instead, prune it by reducing the length of the branches by about one-third. New growth will be produced just behind the cuts. You may want to stagger the lengths of the branches so the tree will have a more normal growth pattern when it develops new stems and branches (as opposed to looking like it got a crew-cut).
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