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In systems with power constraints, context switches in a task schedule result in wasted power consumption. We present variants of priority scheduling algorithms – Rate Monotonic and Earliest Deadline First – that reduce the number of context switches in a schedule. We prove that our variants output feasible schedules whenever the original algorithms do. We present experimental results to show that our variants significantly reduce the number of context switches. Our results also show that the number of context switches in the schedules output by these algorithms is close to the minimum possible number.