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Constraints in classical Optimality Theory are supposedly independent and simple. However, complex constraints are called for to capture significant linguistic generalizations, and local conjunction of constraints has been proposed as one mechanism to derive a complex constraint from simple constraints (Smolenky 1995). This paper aims to show that at least one additional interaction of constraints deriving a complex constraint is needed. I argue that this complex constraint C1*C2 is distinct from Smolensky’s local conjunction in that it requires simultaneous satisfaction of conjunct constraints. Stress pattern in Gugu Yalanji, blends in English and suffixing infixation in Korean are analyzed using the new type of complex constraint. The conspiracy among simple constraints is suggested as the driving force to derive complex constraints to capture linguistic generalizations in phonology and morphology.