We observe that residual claimancy can be a source of rent in a principal-agent relationship. We show that the choice between input or output monitoring will be chiefly determined by the identity of the residual claimant of the principal-agent relationship. The principal will find input monitoring more efficient if the principal is the residual claimant, and he will find output monitoring more efficient if the agent is the residual claimant. If residual claimancy is a choice, the principal will be the residual claimant under input monitoring. Under output monitoring, residual claimancy is not an issue. If both residual claimancy and the monitoring instrument can be chosen, the principal will choose to monitor input and to be the residual claimant. Journal of Economic Literature Classification Numbers: D23, D82, L22.