Structural international theory has become largely a matter of elaborating “the effects of anarchy.” Simple hunter-gatherer band societies, however, perfectly fit the Waltzian model of anarchic orders but do not experience security dilemmas or warfare, pursue relative gains, or practice self-help balancing. They thus demonstrate that “the effects of anarchy,” where they exist, are not effects of anarchy—undermining mainstream structural international theory as it has been practiced for the past three decades. Starting over, I ask what one needs to differentiate how actors are arranged in three simple anarchic orders: forager band societies, Hobbesian states of nature, and great power states systems. The answer turns out to look nothing like the dominant tripartite (ordering principle, functional differentiation, distribution of capabilities) conception. Based on these cases, I present a multidimensional framework of the elements of social and political structures that dispenses with anarchy, is truly structural (in contrast to the independent-variable agent-centric models of Waltz and Wendt), and highlights complexity, diversity, and regular change in the structures of international systems.