Previous rubber/virtual hand illusion studies have established important constraints for the illusion that an artificial effector becomes part of one's own body (perceived ownership), and that its actions are being caused by oneself (perceived agency). We can take these observed constraints to establish two of three Wegner's (Trends Cogn Sci 7:65-69; Wegner, Trends in Cognitive Sciences 7:65-69, 2003) criteria for the perception of personal agency: priority and consistency, but not Wegner's third criterion-exclusivity. In this study we tested with virtual hand illusion, whether exclusivity (participant is certain who was controlling the virtual effector) can also be established. We manipulated two factors: exclusivity and consistency. Our results show that on both ownership and agency judgments, consistency and exclusivity produced main effects, and the two effects interacted in an underadditive fashion. Taken together, these findings provide support for our suggestion to extend Wegner's agency theory to explain perceived body ownership, which in turn provides an integrative framework for interpreting constraints on ownership and agency illusions.