Flow-sensitive labels used by dynamic enforcement mechanisms might themselves encode sensitive information, which can leak. Metalabels, employed to represent the sensitivity of labels, exhibit the same problem. This paper derives a new family of enforcers-k-Enf , for 2 ≤ k ≤ ∞-that uses label chains, where each label defines the sensitivity of its predecessor. These enforcers satisfy Block-safe Noninterference (BNI), which proscribes leaks from observing variables, label chains, and blocked executions. Theorems in this paper characterize where longer label chains can improve the permissiveness of dynamic * Kozyri and Schneider are supported in part by AFOSR grant F9550-16-0250 and NSF grant 1642120. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of these organizations or the U.S. Government. Bedford, Desharnais, and Tawbi are supported by NSERC grants RGPIN-239294-2012 and RGPIN-04461-2015.