A couple of years ago (maybe 3?), I had a customer with a wheat field that had Star-of-Bethlehem in it.  We sprayed it with Harmony Extra - full rate - and it did a surprisingly good job on it.

I have another customer with a good size patch of star-of-Bethlehem in it.  Every spring it comes up, and after the corn is planted and sprayed, it does not seem to be a problem the rest of the season.  I suspect the atrazine we've been using (in Bicep, etc.) is probably having some effect on it.