We formulate four alternative Bayesian models of causal strength judgments, and compare their predictions to two sets of human data. The models were derived by factorially varying the generating function for integrating multiple causes (based on either the power PC theory or the ΔP rule) and priors on strengths (favoring necessary and sufficient (NS) causes, or uniform). The models based on the power generating function provided much better fits than those based on the linear function. The models that included NS priors were able to account for subtle asymmetries between strength judgments for generative and preventive causes.