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Real-time systems are often designed using a set of periodic tasks. Task periods are usually set by the system requirements, but deadlines and computation times can be modified in order to improve system performance. Sensitivity analysis in real-time systems has focused on changes in task computation times using fixed priority analysis. Only a few studies deal with the modification of deadlines in dynamic-priority scheduling. The aim of this work is to provide a sensitivity analysis for task deadlines in the context of dynamic-priority, preemptive, uniprocessor scheduling. In this paper, we present a deadline minimization method that computes the shortest deadline of a periodic task. As undertaken in other studies concerning computation times, we also define and calculate the critical scaling factor for task deadlines. Our proposal is evaluated and compared with other works. The deadline minimization proposed strongly reduces jitter and the response time of control tasks, which can lead to a significant improvement in system performance.