Answer: Along with trees, you might want to consider a trellis with deciduous climbing vines to help shade your deck. Some of the most well-behaved 'patio trees' (so named because they don't have many bad habits), include paperbark maple, trident maple, dogwood, stewartia and crape myrtle. Acacia, laburnum (golden chain) and fruitless mulberry, might be nice too. In my experience, fruitless mulberry provides the densest shade and the leaves are large enough to make end of season raking easier.
Best wishes with your garden!
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