Data centers are increasingly becoming significant energy consumers worldwide. To reduce the amount of electricity they consume, power capping may be used to set a limit to the maximum power they can use at some given point in time. In this situation, an interesting problem is how to make best use of the available power by throttling the CPU frequency of different servers. As different tasks assigned to each of these servers may not be impacted the same way when changing a server’s CPU frequency, one problem that arises is how to select CPU frequencies for each of the servers running tasks with specific characteristics in such a way that the total execution time of all these tasks is minimized while the overall power cap for all the servers is respected. The paper presents an approach that models this problem as an optimization problem and shows how to find an optimal solution in different cases. This work can provide the basis to find economical solutions to operate large data centers under power capping efficiently.