How to make a copy of a list

when copy-list or copy-tree are not deep enough?
I have a big list and I need a function that returns one of its
branches depending on condition.
Later on, in another function I use that branch and modify it
(appending other lists to it).
Now, even though I return that branch using copy-tree, still when I
modify that branch, it modifies the original tree.
Is it because copy-tree only copies conses but not the atoms
themselves?
How can I do a deep copy of the list so it creates a completely new
instance of that branch?

Thank you,
Andrew
.

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