As I mentioned, it blooms in three stages. The first stage is in the late Spring or early Summer. The flowers are white and very aromatic -- they almost smell like gardenias. Here is a photograph of the first stage.
The white flowers then fall off, and these pods -- looking almost like Chinese lanterns, form.

And during the late Fall, the lanterns open to display what appear to be star-shaped flowers, with a fruit in the center. In this photograph, the lantern is just opening up. The berry will true from green to a bluer shade.
Do any of you have any idea what this tree -- actually, it is more like a gangly shrub -- might be?