Display menu link for authenticated users only

What I am trying to do is to create a link in my Main Menu which links to my CiviCRM membership sign up page. The only gotcha is that this link should by made available only to authenticated users. (As a minor aside - this link appears within a drop down menu, which has other links that are available to anonymous users.)

My first approach was to not allow anonymous users access to the CiviContribute page. However, the menu link still appeared (but clicking it resulted in an Access Denied for an anonymous user).

Based on some searching, another suggested approach was to create the link in the User Menu. However, when I select the desired parent menu, the link simply appears in the Main Menu and not in the Use Menu. I tried flushing all caches, but that did not help. When I select as the parent, the link seems to be created, but since the User Menu is not displayed, this doesn't help.

I do have the content-access module installed, but it does not seem to provide the ability to set access control for menu items.

Please help me resolve this matter - I believe that it is the only issue that needs to be resolved for the new membership system to go live.