Each of the six C. elegans vulval precursor cells (VPCs) has three potential fates (1 degree, 2 degrees, or 3 degrees). The fate of each VPC depends on two types of signals: a graded inductive signal that acts at a distance and a short-range lateral signal among the VPCs. We describe interactions among mutations that cause different misspecifications of VPC fates. Particular combinations of mutations cause all six VPCs to have a single fate independent of their positions. Our results suggest that specification of the three VPC fates is accomplished by two binary decisions, each effected by one of the two signaling pathways. The gene lin-12 acts in the lateral signaling pathway and specifies 2 degrees. The "vulvaless" and "multivulva" genes act in the inductive signaling pathway and specify 1 degree independently of lin-12 and 2 degrees via lin-12. We describe a model for the regulatory circuitry underlying VPC determination that includes a role for lin-12 in both autocrine and paracrine VPC signaling.