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Combining high performance with low power consumption is becoming one of the primary objectives of processor designs. Instead of relying just on sleep mode for conserving power, an increasing number of processors take advantage of the fact that reducing the clock frequency and corresponding operating voltage of the CPU can yield quadratic decrease in energy use. However, performance reduction can only be beneficial if it is done transparently, without causing the software to miss its deadlines. In this paper, we describe the implementation and performance-setting algorithms used in Vertigo, our power management extensions for Linux. Vertigo makes its decisions automatically, without any application-specific involvement. We describe how a hierarchy of performance-setting algorithms, each specialized for different workload characteristics, can be used for controlling the processor's performance. The algorithms operate independently from one another and can be dynamically configured. As a basis for comparison with conventional algorithms, we contrast measurements made on a Transmeta Crusoe-based computer using its built-in LongRun power manager with Vertigo running on the same system. We show that unlike conventional interval-based algorithms like LongRun, Vertigo is successful at focusing in on a small range of performance levels that are sufficient to meet an application's deadlines. When playing MPEG movies, this behavior translates into a 11%-35% reduction of mean performance level over LongRun, without any negative impact on the framerate. The performance reduction can in turn yield significant power savings.