How do I make trees sway in the wind?

I just finished making a couple trees in the tree creator tool in Unity.

I added a wind zone and the leaves are shaking. Good!

But, for some reason, the entire tree trunk is completely solid. This is a palm tree. I want to see the entire thing bend in the wind.

How would I get it to do that without a terrain in the scene?

In the inspector of the terrain, if you click add tree, a little drop down box shows up. Choose edit tree. A window opens with the name of the prefab and bend factor.

Give it a value. Consider this action quite expensive so avoid large number. Start with 2 and see the effect on your game and if it looks ok.

You might have to go back to the inner parts of the creation of the tree, http://unity3d.com/support/documentation/Components/tree-Branches.html.

See the animation part at the bottom and you might find what you need.