I answered my own question, sort of. I guess I'm still getting used to doing JSF UI's after doing Struts for so long.
Anyway, I decided to use the standard JSF valueChangeListener to fire
off a ValueChangeEvent in my backing bean.
So, the attributes in my h:selectOneMenu are:
immediate="true" onchange="this.form.submit( );"
valueChangeListener="#{myBacking.myChange}"
This is a good article for reference: http://www.onjava.com/lpt/a/5067
Cheers,
Kevin

