Self Sorting Listbox

Totally stumped by something that seems easy, and has been done to death... Yet still stumped.

What I want to do: I've got a WinForms ListBox. Its items are populated with objects, the DisplayMember is set. As the app runs, the data in the listed items might change, including the field behind the DisplayMember. I want the text displayed in the ListBox to change when this happens, and I also want the ListBox to re-sort itself so the items remain in alphabetical order.

A BindingList works fine to update the displayed text when the data changes, but for the life of me, I can't get it to sort.

I reviewed this: http://msdn.microsoft.com/en-us/library/ms993236.aspx

Plus numerous threads here about how to do this, but none of it seems to work for a ListBox.

Setting the Sorted property on the ListBox is similarly unhelpful.

What do I need to do to get a ListBox to sort itself?