make message private on facebook?

[Anthem]

You can change it through either your account settings or the lock looking button next to your name. To change from settings, click on account settings. Then go to Privacy. There will be a heading titled "Who can contact me?" Change your filtering from basic to strict. To change from the "Lock" button, click on the "Who can contact me?" option which is the second one. Click on Strict filtering. The second way I suggested is the quickest way to change your settings, but either way will get you to where you want as you can see.

I think people can still message you, but you will neither get a notification nor see it in your inbox. The message would go to your "Other" box. I'm not entirely sure though because mine is set up so that anyone can send me a message. I know what you are talking about, but I'm not sure if that is even available anymore, where the message button isn't even shown when someone not on your friends list is viewing your profile. Hope this helps