russian expression

I am looking for a Russian translation of the activity of pruning away dead wood and dead branches from a tree.

A friend of mine suggested the following translation:

обрезка деревьев

I was quite happy with it, but later on I looked after the same issue but would have liked THREE Russian words. Is the following translation acceptable?

обрезка сухостойное деревьев

I thank you very much in advance for your opinion, reply or correction.
Best Regards,
jspriet

I think "обрезка сухостоя" is all you need, really. I don't think we say "сухостойные деревья", "сухостой" sounds more natural to me.

Thank you for your advice