Dynamic information-flow tracking (DIFT) is useful for enforcing security policies, but rarely used in practice, as it can slow down a program by an order of magnitude. Static program analyses can be used to prove safe execution states and elide unnecessary DIFT monitors, but the performance improvement from these analyses is limited by their need to maintain soundness.In this paper, we present a novel optimistic hybrid analysis (OHA) to significantly reduce DIFT overhead while still guaranteeing sound results. It consists of a predicated whole-program static taint analysis, which assumes likely invariants gathered from profiles to dramatically improve precision. The optimized DIFT is sound for executions in which those invariants hold true, and recovers to a conservative DIFT for executions in which those invariants are false. We show how to overcome the main problem with using OHA to optimize live executions, which is the possibility of unbounded rollbacks. We eliminate the need for any rollback during recovery by tailoring our predicated static analysis to eliminate only safe elisions of noop monitors. Our tool, Iodine, reduces the overhead of DIFT for enforcing security policies to 9%, which is 4.4x lower than that with traditional hybrid analysis, while still being able to be run on live systems.