This paper presents a method that enables highspeed, steady flight in confined spaces for tethered quadrocopters. Thanks to the centripetal force exerted by the tether, high-speed trajectories along circles at different velocities, accelerations, and orientations in space can be flown. Various circular maneuvers are experimentally demonstrated, and tangential velocities of up to 15 m/s and centripetal accelerations of more than 13 g can be achieved in steady flight. The recorded data allows to characterize the flight behavior of quadrocopters at high airspeeds: As an example, an estimate of the actual thrust produced by the motors and of the aerodynamic drag acting on the vehicle is presented. An accompanying video shows tethered quadrocopters performing high-speed maneuvers.