In a Computational Grid, or Grid, a user often requires a service to perform an action on his behalf. Currently, the user has few options but to grant the service the ability to wholly impersonate him, which opens the user to seemingly unbounded potential for security breaches if the service is malicious or errorful. To address this problem, eight approaches are explored for realizable, practical, and systematic restricted delegation, in which only a small subset of the user’s rights are given to an invoked service. Challenges include determining the rights to delegate and easily implementing such delegation. Approaches are discussed in the context of Legion, an object-based infrastructure for Grids. Each approach is suited for different situations and objectives. These approaches are of practical importance to Grids because they significantly limit the degree to which users are subject to compromise.