This note discusses fault tolerance in linear finite-state machines (LFSMs). By replacing a given LFSM with a larger, redundant LFSM that preserves the state of the original one in some linearly encoded form, various alternatives to modular redundancy are considered. We characterize the class of appropriate redundant machines in terms of added dynamics and their coupling with the dynamics of the original machine, and illustrate how these can be chosen to minimize redundant hardware.