Answer: Carrot Wood, or Cupaniopsis anacardioides, are slow to moderately slow growing trees native to Australia. They're neat in appearance and are not reputed to have invasive roots, but the fruit drop from mature trees can result in a mass of seedlings below the tree. Carrot Wood can grow to 40' at maturity but take they well to heavy pruning so you can keep the trees somewhat smaller with regular pruning.
Other suggestions include trees of smaller adult height, often referred to as patio trees. You might also consider Acer circinatum (vine maple), Bauhinia forficata (Brazilian Butterfly Tree), Chilopsis linearis (Desert Willow - note: not a true willow so invasive roots are not a problem), Cornus kousa (dogwood), Davidia involucrata (Dove Tree), Albizia julibrissin (Silk Tree), Laburnum (Goldenchain), Sophora japonica (Japanese Pagoda) or Acacia baileyana.
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