Ok, I assume I am just over looking something simple. That said, how do you delete private messages in 4.0? All I see in the messages tab is leave and turn off notifications. 

You can only leave it, you can't delete it.

Once all participants left, the system will delete it automatically.

I doubt that people will leave discussions. This is not so intuitive for many. I think Inbox section of IPS needs some rethinking...