Problems with menus: hiding items and failed links

I'm having problems setting up menus that achieve the following:

1) don't appear unless a permitted user is logged-in
2) the pages in the menu go to the linked pages

I figured I was doing everything right, specifying that the top level menu item appears in a protected group, that I'd selected the appropriate page from the Membership 2 Memberships list to put as a 2nd level menu item.

The menu items appear even when the user is not logged in. And, when he is, and clicks on a link to a page he has access to, he gets redirected to the default 404 page.