We review the logic underlying margin-free analyses of sex segregation arrays. In the course of our review, we show that the Karmel-MacLachlan decomposition does not live up to its margin-free billing, as the index upon which it rests, Ip, is itself margin-sensitive. Moreover, because the implicit individualism of D is necessarily inconsistent with margin-free analysis, the field would do well to abandon not merely the Karmel-MacLachlan decomposition but all related efforts to purge marginal dependencies from D-inspired measures. The criticisms that Watts (1998) levels against our log-multiplicative approach are likewise unconvincing. We demonstrate that our preferred models pass the test of organizational equivalence, that the “problem⤎ of zero cells can be solved by applying well-developed methods for ransacking incomplete or sparse tables, and that simple log-multiplicative models can be readily devised to analyze disaggregate arrays. We illustrate these conclusions by analyzing a new cross-national archive of detailed segregation data.