The dependency core calculus (DCC) is a simple extension of the computational lambda calculus, that captures a common notion of dependency that arises in many programming language settings. This notion of dependency is closely related to the notion of information flow in security; it is sensitive not only to data dependencies that cause explicit flows, but also to control dependencies that cause implicit flows. In this paper, we study variants of DCC in which the data and control dependencies are decoupled. This allows us to consider settings where a weaker notion of dependency---one that restricts only explicit flows---may usefully coexist with DCC's stronger notion of dependency. In particular, we show how strong, noninterference-based security may be reconciled with weak, trace-based security within the same system, improving soundness of the latter and completeness of the former.