A method of processing data using a data processor having an operating system for performing tasks of an application program, and a power and performance controller controlling parameters and modes of execution of the tasks by the data processor. The power and performance controller includes a performance predictor producing an estimation of required performance of the data processor for the tasks taking account of inactive periods of the tasks and adjusting the performance and power consumption of the data processor in response to the estimation. The performance predictor distinguishes for each of the tasks between: —available inactive periods of the task during which the operating system is available to continue to process the same task, and—unavailable inactive periods of the task during which the operating system is not available to continue to process the same task. A substantial improvement is obtained in quality of service, with fewer missed deadlines in performance of the tasks.