Agreed, nice tree indeed.
My live oaks just dropped their leaves and got replaced with new ones the past couple of weeks. If it is a live oak (or similar), I bet you can partially defoliate it safely as Paul suggested.
BTW, I bought a live oak last week...chopped it to a stump and did the same with the roots. From 8 feet nursery tree down to less than 12" (including pot). We will see if it survives.
I did the same on another but smaller one last year...it is doing okay now.