[development] Controlling login/logout in a menu

I'm using the secondary menu to put a few links at the top right of the screen. Among them should be login (if not already) and logout (if logged in). Adding them to the menu is, of course, not an issue, but how would I control their appearing or not based on whether the user is logged in? I was going to use hook_menu_alter, but for some odd reason it doesn't fire when I'm not on an admin page. Something tells me this is going to be a forehead slapping moment, it seems so trivial, but it's eluding me.