Techniques for facilitating a client's control over use of computing-related resources on the client's behalf. In some situations, a client's control is based on specifying a group of one or more resource usage constraints with a client resource constraint manager service, which provides information about the client-specified constraints to one or more other remote network services with which the client interacts. Those remote services then use that constraint information to determine whether and how to use computing-related resources on the client's behalf. For example, the resource usage constraints specified by a client may relate to one or more particular geographical areas and/or to one or more measures of relative proximity between computing-related resources (e.g., between multiple instances of a single type of computing-related resource provided by a single service, or between multiple distinct types of computing-related resources provided by multiple unaffiliated services).