This paper proposes an expansion of set of primitive constraints available within the Primitive Optimality Theory framework <cite>(Eisner, 1997a)</cite> . This expansion consists of the addition of a new family of constraints--existential implicational constraints, which allow the specification of faithfulness constraints that can be satisfied at a distance--and the definition of two ways to combine simple constraints into com: plex constraints, that is, constraint disjunction (Crowhurst and Hewitt, 1995) and local constraint conjunction (Smolensky, 1995) .