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We consider a blocking (i.e., bufferless) flowshop that repetitively processes a minimal part set to minimize its cycle time, or equivalently to maximize its throughput rate. The best previous heuristic procedure solves instances with 9 machines and 25 jobs, with relative errors averaging about 3% but sometimes as much as 10%. The idea of deliberately slowing down the processing of operations (i.e., increasing their processing times) establishes a precise mathematical connection between this problem and a no-wait flowshop. This enables a very effective heuristic for the no-wait flowshop to be adapted as a heuristic for the blocking flowshop. Our computational results show relative errors that average less than 2% for instances with 20 machines and 250 jobs.