In a shared navigable workspace that is presented at more than one workstation, a region is made private in response to a user request. The user can also indicate the region's level of privacy by indicating levels of access of different users. The private region's contents are displayed only to users that have visual access; a non-informative pattern covers the region's area on the displays of other users. The private region and its contents can be modified only by a user with access to modify. When a user requests movement of a pointer into the private region, the pointer can be presented in the private region if the user has sufficient access; otherwise, the pointer would be kept outside the private region's boundary. If a user requests a transition into the private region by selecting a selectable transition unit, called a teleporter, the request would be denied unless the user has sufficient access. The pointer can operate according to a physical metaphor in which it picks up, holds, and puts down other objects, and the user can be permitted to move an object into the private region or to pick up an object within the private region only if the user has sufficient access. Within such a metaphor, a key display object held by a user's pointer can indicate that the user has sufficient access to move the pointer into a corresponding private region; if the user's pointer is not holding the key, it cannot move into the private region.