JavaFX 2.0 :: Sizing Width Of ComboBox Based On Items

I have a ComboBox -- just a simple ComboBox with string items.
 
My string items aren't very long (5 letters max), but the ComboBox shows quite wide relative to my strings. So I would like to size my ComboBox to the size of my strings.
 
I messed around with setting the CellFactory of the ComboBox, and have the Cells produced by the CellFactory set the preferred width of the cells to some constant like 100. That worked in terms of changing the size of the ComboBox to the preferred width of 100.
 
But what I really want to do is to compute the preferred width from the string items. For that I need to be able to compute how wide a string item will be when rendered. And I guess that depends on the font size used by the ComboBox to render strings, which probably depends on the platform (OS X different to Windows?).