This paper points out that previous models for confirmer signature schemes are too restricted to address the case where several signers share the same confirmer. More seriously, we show that various proposed schemes (some of which are provably secure in these restricted models) are vulnerable to an adaptive signature-transformation attack. We define a new stronger model that covers this kind of attack and provide a generic solution based on any secure ordinary signature scheme and public key encryption scheme. We also exhibit a concrete instance thereof.