—This paper seeks to answer fundamental questions about trade-offs between static and dynamic security analysis. It has been previously shown that flow-sensitive static information-flow analysis is a natural generalization of flowinsensitive static analysis, which allows accepting more secure programs. It has been also shown that sound purely dynamic information-flow enforcement is more permissive than static analysis in the flow-insensitive case. We argue that the step from flow-insensitive to flow-sensitive is fundamentally limited for purely dynamic information-flow controls. We prove impossibility of a sound purely dynamic information-flow monitor that accepts programs certified by a classical flow-sensitive static analysis. A side implication is impossibility of permissive dynamic instrumented security semantics for information flow, which guides us to uncover an unsound semantics from the literature. We present a general framework for hybrid mechanisms that is param...