Our "Visible To" interface looks like this:
The first part says the ticket is public, but in this case it actually isn't. Frankly I've never understood what the first select list is for, but I've never used it and it doesn't seem to be helpful. Whenever I'm training new hires I tell them to just ignore the first select list and use the second.
What is the first select list actually for? Do we need it? If so, can the options be changed to be more accurate/less confusing?