Question about discrete opfibrations

Suppose D is a finite category. Does there exist a unique discrete opfibration (dof) p:D->C such that C has a minimal number of objects? (With "unique", I mean that any two dofs p:D->C and p':D->C', where C and C' have the minimal number of objects, are isomorphic in the sense that there exists an isomorphism i:C->C' such that p' = ip) If so, is there an efficient algorithm to compute this discrete opfibration? If not so, can you give a counter-example? Thanks in advance for any replies, Frank Piessens Katholieke Universiteit Leuven. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++