In their seminal paper, Geis and Zwicky (1971) drew attention to "a tendency of the human mind ... to 'perfect conditionals to biconditionals'". They used the material conditional -> for their analysis and suggested the following principle: "A sentence of the form A -> C invites an inference of the form ~A -> ~C.'' It has been pointed out in the literature that there are several non-equivalent ways of understanding conditional perfection. In my talk I follow suit and examine four possible ways of implementing conditional perfection. Proceeding on the assumptions that (i) the perfecting of conditionals should be based on suppositional conditionals (of the kind studied in the tradition of Ramsey, Adams, Stalnaker and Lewis) rather than material conditionals, and that (ii) this perfecting occurs at the primary level of meaning, I will study the logics of these interpretations. The four logics turn out to be significantly different, but they are unified in invalidating the inference scheme of Weakening the Consequent.