Desert Olive (Forestiera neomexicana) is not the same plant as the olive tree (Olea europaea) you may be familiar with, but it gets its name from the fruits that resemble true olives. The blackish-purple fruits are not always present, and are unpredictable as some plants do not have both male and female flowers. The fruits do attract birds when they are present and can be messy.
Desert Olive, unlike the real thing, is deciduous. It can either be a large shrub or small tree. To make tree like it will need to be pruned into tree form up to 18 feet tall and 12 feet wide. The Desert Olive needs full sun and little to moderate water. It is fast growing, making it a good summer shade tree.
As a side note, Olea europea, the true olive, is a prohibited tree in the Tucson area because of the pollen it produces. There is a non-fruiting variety; but those are not predictably ‘non-fruiting’.
Reference: Sunset Western Garden Book, Sunset Publishing Corp. 2001