Robustness links confidentiality and integrity properties of a computing system and has been identified as a useful property for characterizing and enforcing security. Previous characterizations of robustness have been with respect to a single idealized attacker; this paper shows how to define robustness for systems with mutual distrust. Further, we demonstrate that the decentralized label model (DLM) can be extended to support fine-grained reasoning about robustness in such systems. The DLM is a natural choice for capturing robustness requirements because decentralized labels are explicitly expressed in terms of principals that can be used to characterize the power of attackers across both the confidentiality and integrity axes. New rules are proposed for statically checking robustness and qualified robustness using an extended DLM; the resulting type system is shown to soundly enforce robustness. Finally, sound approximations are developed for checking programs with bounded but unknown label parameters, which is useful for security-typed languages. In sum, the paper shows how to use robustness to gain assurance about secure information flow and information release in systems with complex security requirements.