Trimming Yaupon Holly

Hi,
I was hoping to get some advice on this issue ..
My hollies need trimming again, but before I do it, I'd like to get some feedback.
I just trimmed it about 6-8 weeks ago, and the new growth is starting to get raggedy, so I think it is time again.
I've noticed that the new growth is a vibrant beautiful light green, and the older leaves underneath are dark green.
Every time I trim it, I trim it back to the old growth- these leaves are just getting older and older. Is it hurting the tree any that I am continually removing its new leaves?
Should I be trimming back a few inches past the line of old growth, so that new growth can replace it and then later re-trim at the regular depth?
Thanks ..
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I would leave some of the new growth, but all of my yaupons are in places where I can allow them to grow into their natural shape.

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