|Abstract:||One of the fundamental original assumptions of Optimality Theory (Prince and Smolensky 1993) is that of strict domination: once a candidate is eliminated from consideration by Eval, it cannot be resurrected, no matter how much better it fares than its competitors on lower-ranked constraints. However, the well known proposal of local constraint conjunction (Smolensky 1993, 1995, 1997) qualifies this basic assumption. The basic idea of constraint conjunction is that two or more violations of some constraint(s) may 'gang up' in a particular way, violating a separate, higher-ranked constraint. Because it explicitly relinquishes the assumption of strict domination, constraint conjunction represents an important departure from the more restrictive original conception of constraint ranking. Further, constraint conjunction faces well known challenges of potential overgeneration. Though there have been several proposals about how to address these challenges, no consensus has emerged. In this paper, I examine several significant uses of constraint conjunction that have been proposed, and suggest that they all can and should be subsumed under a notion independently required, that of the universal constraint subhierarchy (Prince and Smolensky 1993). If this is correct, then constraint conjunction is not required of the theory. In addition, following Prince and Smolensky, I take universal subhierarchies to be derived from linguistically relevant scales. Assuming these are phonetically or psycholinguistically grounded, then we have a promising means by which to address the challenge of overgeneration.