We provide a formal security model for traceable attribute-based signatures. Our focus is on the more practical case where attribute management is distributed among different authorities rather than relying on a single central authority. By specializing our model to the single attribute authority setting, we overcome some of the shortcomings of the existing model for the same setting. Our second contribution is a generic construction for the primitive which achieves a strong notion of security. Namely, it achieves CCA anonymity and its security is w.r.t. adaptive adversaries. Moreover, our framework permits expressive signing polices. Finally, we provide some instantiations of the primitive whose security reduces to falsifiable intractabili...