I want to reduce the overall size of a 30 year old Burford holly. It's now done blooming and set another huge crop of berries ( which I have pruned off a lot of, because birds never ate last year's crop.) Can I cut back to bare wood now, mid May, and expect some.branching out? It's about fifteen feet tall and ten wide, much too big for the place I put it, be cause I had no sense of how big it could get, and underestimated my energy for keeping it pruned back every year.

For best results... Prune hard in Feb or march before new growth and flowering.
Your birds didn't eat the berries?
That's not right... Is Taking their food away really the solution?

You can probably cut plants back some... They're tolerant of that kind of thing...
But really wouldn't be my first choice.

https://www.uaex.uada.edu/yard....
Unpruned, plants may be as wide as they are tall but they tolerate shearing well and their size can be kept under control by cutting back as needed. Spring, just before new growth begins, is the best time for severe pruning but light pruning can be done at any season.

They had six months to eat those berries and didn't. I don't feel I'm denying them.

Prune it now. There's still plenty of warm weather left for new growth to harden before next winter. Send Stone all the berries.

The thing about the birds and holly berries...
They prefer to wait until the berries are just the right amount of fermented... Then, all the birds in the neighborhood show up and strip the bush in hours...
Pick them off before the berries are ready? Not so good.

As far as cutting back now?
If I was doing it... I'd wait.

Not sure Lucy understands that you are talking about drastic cutting back, below where the bush has been sheared...