We address the problem of designing very high-throughput finite-state machines (FSMs). The presence of loops in sequential circuits prevents a straightforward application of pipelining to increase performance. We observe that appropriate extensions of the "wave steering" technique can partially overcome the problem. We find that FSM decomposition theory is useful for decoupling the state-variable dependencies. Experiments on MCNC benchmarks show a 217 percent improvement in throughput, at the expense of a similar increase in area (2.15 times). Latency loss is relatively small, on the order of 20 percent, as compared to standard cell implementations.