Looks like Wax Myrtle, Myrica cerifera.

Christopher, don't these leaf margins look smooth, compared to the serrated leaves of Morella/Myrica cerifera?

I considered Myrica cerifera but that is evergreen and the OP stated this is deciduous. Growth on shrub looks deciduous as well.........

Is it genuinely, fully deciduous? Yes, there is new growth. But there also appear to be older leathery leaves which don’t look brand new to me.

Morella caroliniensis is semi evergreen. The leaves are a better match. It has the same large glands where the petiole meets the stem. OP didn't give height, M. caroliniensis tops out around 8'. The leaves are aromatic when crushed. The leaves can be lobed or unlobed. Previously Myrica heterophylla with 2 varieties curtisii and heterophylla. Morella is the legit name now, only 2 species remain in Myrica.

​Good morning from a frosty NC. Thank you for your thoughtful conversation. I believed it was deciduous because we moved in in December and I don't remember seeing a lot of leaves. But with it being a busy time I may not be accurate in my memory.

The North Carolina gardeners toolbox says that the Myrtle is subject to leaf drop during acclimatization. That may be the case for the Morelka since they're similar. 

Thanks for the ID. This helps me talk to the (not big box) garden folks with some idea of how to care for these.

Yes, the leaf margins do look a bit smooth for Myrica cerifera, but everything else about it says Myrica/Morella - noted and was not sure which was current genus. I just attributed the smooth leaf margins to the vastly increased propagation and selection of this as a landscape plant. Morella caroliniensis may be more exact. The Raleigh location puts it at the northern end of the southern species M. cerifera where it is more likely to be semi-deciduous there.