game center privacy settings question

Hi. On game center, is there a way to make it so my friends can't see all my other friends? In the game center settings, I saw the option to turn the public profile on or off, but it says that even if I turn it off, my friends can still see my friends. I don't like that, so I had to remove some people. I would like to be able to re-ad them, but in a way that they can only see me and my games and not be able to view my list of friends. I have looked everywhere in the game center app as well as the settings app and I have not found any privacy settings other then the one public profile one, but like I said, if I turn that off, my friends can still see my other friends. Is there anything I can do about this? Thank you. Also, if anyone wants to ad me, my user name is JessicaBrown531