The rules of person agreement in languages of the Dargwa group (North-East Caucasian) are complex and based on the relative prominence of the core arguments on the personal and grammatical function hierarchies. The rules are also subject to much cross-dialectal variation. I argue that this variation can best be captured by assuming that the agreement marker specifies the person and number of an m-structure function called TH, which can be identified with either of the core arguments. The choice of agreement controller is determined not by functional annotations, but by four OT constraints: Th-1, Th-2, Th-GF and Th-ABS. Thus the same f-structure maps to different c- and m-structure pairs in different Dargwa varieties based on variation in constraint orderings. This allows capturing cross-dialectal variation in a uniform way while providing generalizations about which of the logically possible agreement systems are actually attested.