How do I get a list of visible nodes in a Flex tree?

I have a base tree built in Flex. The tree works fine. I am trying to get a list of all visible nodes. I know there is Tree.openItems, but that is not enough, since (for example) if you open all items in your tree and then close the root directory, invisible open items are still counted.

I just want a list of all visible items. Any help would be greatly appreciated!