It is important for applications to protect sensitive data. Even for simple confidentiality and integrity policies, it is often difficult for programmers to reason about how the policies should interact and how to enforce policies across the program. A promising approach is policy-agnostic programming, a model that allows the programmer to implement policies separately from core functionality. Yang et al. describe Jeeves, a programming language that supports information flow policies describing how to reveal sensitive values in different output channels. Jeeves uses symbolic evaluation and constraint-solving to produce outputs adhering to the policies. This strategy provides strong confidentiality guarantees but limits expressiveness and implementation feasibility. We describe a new language Jeeves* that provides the same guarantees while exploiting the structure of sensitive values to yield greater expressiveness and to facilitate reasoning about runtime behavior. We present a semantics based on Austin et al.'s faceted execution describing a model for propagating multiple views of sensitive values through a program. We provide a proof of termination-insensitive non-interference and describe how the semantics facilitate reasoning about program behavior.