Model predictive control (MPC) is an established and acclaimed method. Because MPC is based on solving an optimal control problem (OCP) in every sampling interval, MPC incurs costly calculations at runtime, however. Consequently, a lot of research effort has been and still is devoted to reducing the computational effort of MPC. Most approaches attempt to reduce the maximum computing time of the underlying OCP because of the immediate importance of this quantity for realtime applicability of MPC. In contrast, we devote our efforts to reducing the computational effort of MPC on average or in the large in the present paper, because the average computing time determines the average power requirements of MPC, which, in turn, are crucial for use of MPC in battery-powered devices. Because battery power is a limiting factor for drones, and because control algorithms for drones require sampling times of milliseconds or below, they are an excellent application example. Specifically, we demonstrate that the average computational effort of MPC applied to the hovering control of a quadcopter can be reduced considerably with a technique known as online constraint removal.