Precise numbers are more potent anchors than round ones. Two theoretical
mechanisms have been suggested to account for this anchor precision effect: (1) the scale granularity account postulates that individuals adjust away from the anchor in smaller steps on a finer-grained mental scale, and (2) the attribution-of-competence account postulates that people ascribe more competence to a precise-opening individual. Direct empirical evidence for both accounts is scarce, however, and exists mainly for the attribution-of-competence account in a negotiation context. In two experiments, we examined the two competing mechanisms simultaneously (Experiment 1) and contrasted them in a negotiation and in an estimation context (Experiment 2). Moreover, we developed and validated (Pilot Study) a direct measurement of scale-granularity. Mediation analyses showed that both attribution-ofcompetence and, for the first time, scale-granularity mediate the anchor-precision effect. The results refine our theoretical understanding of anchor precision. Implications for decisionmaking, negotiation, and estimation research are discussed.