Aggregate signature schemes combine the digital signatures of multiple users on different messages into one single signature. The Boneh-Gentry-Lynn-Shacham (BGLS) aggregate signature scheme is one such scheme, based on pairings, where anyone can aggregate the signatures in any order. We suggest improvements to its current chosen-key security model. In particular, we argue that the scheme should be resistant to attackers that can adaptively choose their target users, and either replace other users' public keys or expose other users' private keys. We compare these new types of forgers to the original targeted-user forger, building up to the stronger replacement-and-exposure forger. Finally, we present a security reduction for a variant of the BGLS aggregate signature scheme with respect to this new notion of forgery. Recent attacks by Joux and others on the discrete logarithm problem in small-characteristic finite fields dramatically reduced the security of many type I pairings. Therefore, we explore security reductions for BGLS with type III rather than type I pairings. Although our reductions are specific to BGLS, we believe that other aggregate signature schemes could benefit from similar changes to their security models.