Italian Cypress (Cupressus sempervirens) grows well in Tucson, but I don't think that its dark, formal, columnar style blends well with our natural desert vegetation.
I have a row of three of these towering trees in my yard, and although I'm not too fond of their stiff, formal appearance, they are very popular with the birds who appreciate their dense, evergreen foliage for nesting cover and as shelter on hot summer days.
Almost every year, Greater Roadrunners will nest in one of my Italian Cypress trees. I will also often see juvenile Western Screech-owls roosting in one of these same trees during the day. Despite the fact that both birds are predators, neither seems much bothered by the other's presence in these favored trees.