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Methods for proving that concurrent software does not leak its secrets has remained an active topic of research for at least the past four decades. Despite an impressive array of work, the present situation remains highly unsatisfactory. With contemporary compositional proof methods one is forced to choose between expressiveness (the ability to reason about a wide variety of security policies), on the one hand, and precision (the ability to reason about complex thread interactions and program behaviours), on the other. Achieving both is essential and, we argue, requires a new style of compositional reasoning. We present VERONICA, the first program logic for proving concurrent programs information flow secure that supports compositional, high-precision reasoning about a wide range of security policies and program behaviours (e.g. expressive de-classification, value-dependent classification, secret-dependent branching). Just as importantly, VERONICA embodies a new approach for engineering such logics that can be re-used elsewhere, called decoupled functional correctness (DFC). DFC leads to a simple and clean logic, even while achieving this unprecedented combination of features. We demonstrate the virtues and versatility of VERONICA by verifying a range of example programs, beyond the reach of prior methods.